Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #360 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7181 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #102 |
| commutator | C8 | C4×C8×C11 |
| Frattini, cosocle | C2×C4×C8 | C22×C11 |
| socle | C2×C11 | #1279 |
| prime radical | C23×C11 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,18,23,34,39,19,24,33,40,17,22,15,31)(14,25,27,36,29,42,26,20,30,35,43,37,28,41,32,38);(12,14,17,28,19,30,18,29)(13,20)(15,32,33,43,34,26,16,27)(21,35)(22,36)(23,37)(24,38)(25,40)(31,42)(39,41)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 169);