Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9379 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
492 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)(12,13,16,23,29,39,14,26)(15,31,34,41,43,22,30,38)(17,24,27,19,18,25,28,21)(20,37,35,33,40,42,36,32);(13,19,24,23)(14,27)(15,32)(16,28)(20,35,31,41)(21,25,26,39)(22,38,40,36)(30,34)(33,43)(37,42);(13,20)(14,28)(15,33)(16,27)(19,35)(21,36)(22,25)(23,41)(24,31)(26,38)(30,34)(32,43)(37,42)(39,40)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2367);