Finite Group DatabasebetaFinite Group Databasebeta| order | 31926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D313⋊C3) |
| unambiguous semidirect product | (C313⋊C3)⋊D17 |
| unambiguous semidirect product | D5321⋊C3 |
| Fitting, socle, derived, Hall | C17×C313 ⋊ C2×C3 |
| Hall | C17×C313⋊C3 ⋊ C2 |
| Hall | D5321 ⋊ C3 |
| Hall | C313⋊C3 ⋊ D17 |
| Sylow | C313 ⋊ C3×D17 |
| Sylow | C17 ⋊ D313⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C313 | C2×C3 |
| LCS | G ▷ C17×C313 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 330 |
| transitive degree | μt(G) = 5321 |
A minimal faithful permutation representation — 2 generators on 330 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,23,24,20,21,25)(22,31,32,26,27,41)(28,44,45,34,35,58)(29,43,39,37,33,30)(36,63,64,47,48,81)(38,61,62,50,46,55)(40,42,60,52,53,56)(49,86,87,66,67,110)(51,84,85,69,65,78)(54,59,83,71,72,79)(57,99,97,75,76,74)(68,115,116,89,90,145)(70,113,114,92,88,107)(73,82,112,94,95,108)(77,128,129,100,101,103)(80,134,126,104,105,98)(91,150,151,118,119,186)(93,148,149,121,117,142)(96,111,147,123,124,143)(102,163,164,130,131,138)(106,170,168,135,136,133)(109,175,161,139,140,127)(120,191,192,153,154,233)(122,189,190,156,152,183)(125,146,188,158,159,184)(132,204,205,165,166,179)(137,211,212,171,172,174)(141,217,209,176,177,169)(144,222,202,180,181,162)(155,238,239,194,195,280)(157,236,237,197,193,230)(160,187,235,199,200,231)(167,249,250,206,207,226)(173,254,255,213,214,221)(178,259,257,218,219,216)(182,264,252,223,224,210)(185,269,247,227,228,203)(196,256,268,215,241,292)(198,283,284,242,240,277)(201,234,282,244,245,278)(208,285,289,243,251,273)(220,295,296,260,261,263)(225,298,293,265,266,258)(229,303,290,270,271,253)(232,307,287,274,275,248)(246,281,302,262,286,314)(267,321,319,299,300,297)(272,323,317,304,305,294)(276,324,315,308,309,291)(279,322,301,311,312,288)(306,328,329,316,313,320)(310,330,327,325,326,318);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,19,22,28,36,49,68,91,120,155,196,213,171,135,104,72,35,46,56,58,78,103,133,169,210,253,291,316,304,270,227,159,90,117,131,136,140,143,145,183,226,268,302,322,324,323,321,286,195,240,251,256,261,266,271,275,278,280,289,237,151,188,222,217,211,204,189,150,187,232,276,310,327,317,293,257,212,164,114,64,83,99,84,63,82,109,141,178,220,262,244,199,158,123,94,71,52,39,24,23,29,38,51,70,93,122,157,198,243,206,165,130,100,75,53,27,33,41,55,74,98,127,162,203,248,288,299,265,223,180,124,67,88,101,105,108,110,142,179,221,263,297,320,330,328,311,245,154,193,207,214,219,224,228,231,233,277,284,192,235,269,264,259,254,249,236,191,234,279,313,326,329,319,296,255,205,149,87,112,134,128,113,86,111,144,182,225,267,301,287,247,202,161,126,97,62,32,43,31,42,57,77,102,132,167,208,242,197,156,121,92,69,50,37,21,25,30,40,54,73,96,125,160,201,246,260,218,176,139,95,48,65,76,79,81,107,138,174,216,258,294,318,325,308,274,200,119,152,166,172,177,181,184,186,230,273,239,282,307,303,298,295,241,285,283,238,281,300,305,309,312,314,292,250,190,116,147,175,170,163,148,115,146,185,229,272,306,315,290,252,209,168,129,85,45,60,61,44,59,80,106,137,173,215,194,153,118,89,66,47,34,26,20)Polycyclic presentation:
2,3,17,313|c^a=c^16,d^a=d^312,d^b=d^214914 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31926, 12);