Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11485 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #99 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C2×M16 | C23×C11 |
| socle | C2×C11 | #1459 |
| prime radical | C11×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C2×C8×C11 ◁ C2×C11×#131 ◁ G | |
372 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)(12,13,17,23,18,22,34,40,19,24,35,42,16,32,26,41)(14,25,28,43,27,20,15,21,29,37,30,38,33,36,31,39);(12,14)(13,20)(15,26)(16,33)(17,30)(18,27)(19,29)(21,23)(22,37)(24,36)(25,32)(28,35)(31,34)(38,40)(39,42)(41,43);(12,15,18,30,19,31,16,28)(13,21,22,38,24,39,32,43)(14,26,27,17,29,34,33,35)(20,23,37,40,36,42,25,41)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4473);