Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33702 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(21,27)(22,32)(23,24)(25,36)(29,40)(30,41)(31,45)(33,34)(35,47)(37,38)(39,43)(44,50)(46,48)(49,51);(13,16)(17,19)(20,21,24,30,25,31,37,40,26,29,38,45,36,41,23,27)(22,28,32,43,34,44,46,49,35,42,47,51,48,50,33,39);(12,14,15,18)(13,17,16,19)(20,22,23,33,36,48,38,47,26,35,37,46,25,34,24,32)(21,28,27,39,41,50,45,51,29,42,40,49,31,44,30,43);(21,29)(27,40)(28,42)(30,45)(31,41)(39,49)(43,51)(44,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26690);