Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11984 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21,24,30,26,31,39,29,25,28,40,45,38,46,23,37)(22,32,34,42,36,47,50,49,35,48,51,27,41,43,33,44);(12,13)(14,17)(15,19)(16,18)(20,22,25,35)(21,27,28,42)(23,34,39,51)(24,33,40,50)(26,41,38,36)(29,47,37,43)(30,48,45,32)(31,49,46,44);(12,14,16,15)(13,17,18,19)(21,28)(27,42)(29,37)(30,45)(31,46)(32,48)(43,47)(44,49)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4972);