Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13100 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1898 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C2×#41 | C23×C11 |
| prime radical | C2×C11×H(5,𝔽2) | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×H(5,𝔽2) ◁ G | |
672 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)(12,13,17,20,18,23,16,22)(14,24,28,40,29,42,27,41)(15,30,25,38,32,21,33,35)(19,34,36,31,37,43,39,26);(12,14,25,34)(13,19,35,40)(15,31,17,27)(16,28,32,26)(18,29,33,43)(20,36,21,24)(22,39,30,42)(23,37,38,41);(13,20)(15,32)(16,17)(19,36)(21,35)(22,23)(24,40)(26,31)(27,28)(30,38)(37,39)(41,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6088);