Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C23×C11 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,23,26)(15,19,16,24)(18,25,27,22)(28,29)(30,36)(31,39)(32,35)(33,38)(34,41)(37,43)(40,42);(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(33,42)(36,43);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(28,30)(29,33)(31,40)(32,37)(34,43)(35,42)(36,39)(38,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2991);