Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#8998 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| socle | C22×C11 | #386 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
414 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)(14,21,25,27)(15,24,26,18)(16,19)(17,20)(22,23)(28,29)(30,36,38,43)(31,33)(32,35)(34,37,41,40)(39,42);(12,14,22,24,17,25,16,18)(13,15,23,21,20,26,19,27)(29,33)(32,39)(34,41)(37,40);(12,15)(13,18)(14,23)(16,27)(17,26)(19,25)(20,24)(21,22)(28,30)(29,34)(31,38)(32,40)(33,41)(35,43)(36,42)(37,39)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1986);