Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13417 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2041 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C11×#3155 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,26)(15,20)(16,32)(17,23)(18,22)(19,25)(21,29)(24,34)(27,37)(28,40)(30,38)(31,42)(33,39)(35,41)(36,43);(13,20)(14,27)(15,18)(16,17)(21,38)(22,25)(23,42)(26,41)(28,29)(30,33)(31,34)(35,36)(37,40)(39,43);(12,14,15,28,19,30,18,36)(13,21,22,39,25,41,20,37)(16,33,31,29,34,27,17,35)(23,40,24,26,42,43,32,38)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6405);