Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23399 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C22×C11 | C2×#120 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
2062 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,23)(19,24)(20,28)(21,25)(22,26)(27,30)(29,31);(16,18)(17,22)(19,26)(20,29)(21,27)(23,28)(24,30)(25,31);(13,15)(16,18)(17,23)(19,26)(20,29)(21,27)(22,24)(25,30)(28,31);(16,19,21,20)(17,24,25,28)(18,26,27,29)(22,30,31,23)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16387);