Finite Group DatabasebetaFinite Group Databasebeta| order | 28158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C13×C361 ⋊ C2×C3 |
| Hall | #28381091 ⋊ C2 |
| Hall | D4693 ⋊ C3 |
| Sylow | C361 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C13×C361 | C2×C3 |
| Frattini | C19 | #13093366 |
| socle | C13×C19 | D19⋊C3 |
| LCS | G ▷ C13×C361 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 374 |
| transitive degree | μt(G) = 4693 |
A minimal faithful permutation representation — 2 generators on 374 points:
(2,6,7,3,4,8)(5,11,12,9,10,13)(15,24,26,17,18,27)(16,36,38,21,22,40)(19,53,55,29,30,109)(20,65,66,33,34,136)(23,82,84,41,42,164)(25,74,91,37,45,106)(28,104,76,50,51,156)(31,119,79,58,59,159)(32,129,130,62,63,227)(35,144,145,69,70,253)(39,93,47,77,78,96)(43,114,98,86,56,48)(44,140,141,89,67,80)(46,166,178,83,94,280)(49,72,139,101,102,68)(52,196,168,107,108,283)(54,61,125,75,112,127)(57,207,157,116,117,274)(60,183,92,123,124,172)(64,235,236,133,134,347)(71,262,97,148,149,184)(73,169,163,153,85,81)(87,215,142,171,121,199)(88,186,212,173,131,242)(90,256,257,175,146,266)(95,261,103,165,181,191)(99,110,160,185,161,111)(100,137,230,188,189,231)(105,209,221,170,126,176)(113,281,315,167,202,341)(115,192,249,204,205,303)(118,323,284,210,211,324)(120,187,228,155,213,241)(122,239,240,217,135,352)(128,338,339,224,225,364)(132,200,151,232,233,267)(138,255,277,246,247,162)(143,193,285,251,252,182)(147,243,152,259,260,270)(150,177,250,264,265,291)(154,293,278,248,198,273)(158,263,298,271,180,195)(174,348,349,289,237,358)(179,370,219,294,295,300)(190,254,330,304,305,359)(194,335,331,287,301,220)(197,325,368,286,309,292)(201,306,345,313,314,353)(203,282,312,279,214,365)(206,308,299,319,320,310)(208,226,343,276,229,290)(216,321,356,327,258,362)(218,311,244,272,329,297)(222,369,357,333,334,372)(223,275,268,336,337,317)(234,322,366,346,302,318)(238,342,269,326,351,316)(245,367,328,296,350,354)(288,363,371,355,340,332)(307,361,374,373,360,344);(1,2,5,7,6,10,12,13,11,4,8,9,3)(14,165,276,313,295,185,321,195,248,249,189,74,253,190,130,340,111,324,46,21,285,161,281,344,213,220,106,138,357,296,78,247,100,351,325,53,318,25,41,168,79,268,231,322,349,51,65,362,288,265,146,48,341,216,116,203,17,82,162,337,240,131,207,332,252,139,297,172,261,103,183,225,121,210,113,33,169,80,269,234,335,125,221,250,251,179,87,147,49,300,211,114,235,54,69,84,39,151,132,222,336,205,140,262,174,194,70,27,308,122,204,326,29,148,81,271,157,63,126,347,373,66,180,88,310,52,96,369,59,319,214,62,264,40,152,339,226,60,343,311,260,94,43,360,28,184,292,55,348,120,133,257,22,72,353,128,272,314,199,280,90,105,305,18,196,354,233,367,58,239,273,153,76,241,61,359,312,212,198,44,197,286,89,293,242,365,330,112,228,156,73,278,135,31,350,200,328,108,24,254,170,175,178,142,306,218,224,345,102,36,266,64,155,237,109,368,97,50,361,86,166,243,329,290,123,229,364,270,38,150,32,282,206,119,334,47,107,299,173,263,136,307,236,209,129,274,158,163,71,19,238,115,217,320,26,144,287,289,149,67,192,223,333,232,267,77,164,35,75,134,56,323,219,101,259,171,294,143,291,176,127,301,346,316,141,85,20,167,118,215,338,124,191,181,92,244,68,193,371,117,186,352,275,277,42,15,279,57,327,315,98,256,177,355,356,34,104,358,302,230,317,159,283,23,37,366,30,309,342,188,255,93,245,372,246,91,331,187,374,202,110,182,16,83,284,160,363,227,304,145,45,137,303,154,298,258,99,370,201,208,95)Polycyclic presentation:
2,3,13,19^2|d^19=e^18,c^a=c^12,d^a=d^18e,e^a=e^18,c^b=c^9,d^b=d^11e^16,e^b=e^11788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28158, 12);