Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33558 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,19)(16,20)(17,21)(18,25)(23,35)(24,36)(26,32)(27,33)(28,41)(29,34)(30,37)(31,39)(38,43)(40,42);(12,14,17,24)(13,18,21,31)(15,23,26,38)(16,25,29,39)(19,30,32,42)(20,22,34,36)(27,37,28,40)(33,35,41,43);(12,15)(13,19)(14,23)(16,28)(17,26)(18,30)(20,33)(21,32)(22,35)(24,38)(25,40)(27,29)(31,42)(34,41)(36,43)(37,39);(14,24)(15,26)(18,31)(19,32)(22,36)(25,39)(27,28)(33,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26546);