Finite Group DatabasebetaFinite Group Databasebeta| order | 28626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C367 ⋊ C2×C3 |
| Hall | #28384860 ⋊ C2 |
| Hall | D4771 ⋊ C3 |
| Sylow | C367 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D367⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C367 | C2×C3 |
| LCS | G ▷ C13×C367 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 380 |
| transitive degree | μt(G) = 4771 |
A minimal faithful permutation representation — 2 generators on 380 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,27,28,22,23,37)(24,40,41,30,31,54)(25,39,35,33,29,26)(32,59,60,43,44,77)(34,57,58,46,42,51)(36,38,56,48,49,52)(45,82,83,62,63,106)(47,80,81,65,61,74)(50,55,79,67,68,75)(53,95,93,71,72,70)(64,111,112,85,86,141)(66,109,110,88,84,103)(69,78,108,90,91,104)(73,124,125,96,97,99)(76,130,122,100,101,94)(87,146,147,114,115,182)(89,144,145,117,113,138)(92,107,143,119,120,139)(98,159,160,126,127,134)(102,166,164,131,132,129)(105,171,157,135,136,123)(116,187,188,149,150,229)(118,185,186,152,148,179)(121,142,184,154,155,180)(128,200,201,161,162,175)(133,207,208,167,168,170)(137,213,205,172,173,165)(140,218,198,176,177,158)(151,234,235,190,191,282)(153,232,233,193,189,226)(156,183,231,195,196,227)(163,247,248,202,203,222)(169,254,255,209,210,217)(174,261,259,214,215,212)(178,266,252,219,220,206)(181,271,245,223,224,199)(192,287,288,237,238,339)(194,285,286,240,236,279)(197,230,284,242,243,280)(204,299,300,249,250,275)(211,306,307,256,257,270)(216,313,314,262,263,265)(221,319,311,267,268,260)(225,324,304,272,273,253)(228,329,297,276,277,246)(239,344,345,290,291,379)(241,342,343,293,289,337)(244,283,341,295,292,338)(251,350,351,301,302,333)(258,355,356,308,309,328)(264,360,361,315,316,323)(269,365,363,320,321,318)(274,368,358,325,326,312)(278,371,353,330,331,305)(281,374,349,334,335,298)(294,375,354,336,346,377)(296,340,380,347,348,378)(303,372,359,332,352,376)(310,369,364,327,357,373)(317,366,367,322,362,370);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,18,24,32,45,64,87,116,151,192,239,292,191,236,250,257,263,268,273,277,280,282,337,376,358,311,259,208,160,110,60,79,95,80,59,78,105,137,174,216,264,317,320,267,219,176,120,63,84,97,101,104,106,138,175,217,265,318,364,351,286,188,231,271,266,261,254,247,232,187,230,281,336,293,240,193,152,117,88,65,46,33,17,21,26,36,50,69,92,121,156,197,244,296,348,238,289,302,309,316,321,326,331,335,338,339,377,353,304,252,205,164,125,81,41,56,57,40,55,76,102,133,169,211,258,310,325,272,223,155,86,113,127,132,136,139,141,179,222,270,323,367,356,300,233,147,184,218,213,207,200,185,146,183,228,278,332,301,249,202,161,126,96,71,49,23,29,37,51,70,94,123,158,199,246,298,345,380,291,346,352,357,362,366,369,372,375,344,378,379,349,297,245,198,157,122,93,58,28,39,27,38,53,73,98,128,163,204,251,303,330,276,196,115,148,162,168,173,177,180,182,226,275,328,370,361,307,248,186,112,143,171,166,159,144,111,142,181,225,274,327,308,256,209,167,131,100,68,31,42,52,54,74,99,129,165,206,253,305,354,288,341,374,371,368,365,360,355,350,342,287,340,347,295,242,195,154,119,90,67,48,35,20,19,25,34,47,66,89,118,153,194,241,294,334,243,150,189,203,210,215,220,224,227,229,279,333,373,363,314,255,201,145,83,108,130,124,109,82,107,140,178,221,269,322,315,262,214,172,135,91,44,61,72,75,77,103,134,170,212,260,312,359,343,235,284,329,324,319,313,306,299,285,234,283,290,237,190,149,114,85,62,43,30,22,16)Polycyclic presentation:
2,3,13,367|c^a=c^12,d^a=d^366,c^b=c^3,d^b=d^83801 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28626, 24);