Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#11401 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C11 | C23 |
| commutator | C22 | C2×C4×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×C4×C8 |
| prime radical | C23×C11 | C4×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C11 ◁ G | |
298 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)(12,13,14,17,15,16,18,19)(20,21)(22,26)(23,28)(24,29)(25,27)(30,37)(31,38)(32,36)(33,41)(34,39)(35,40)(42,48)(43,46)(44,47)(45,49)(50,51);(13,16)(17,19)(20,22,23,30,24,31,33,42,25,32,34,43,35,44,45,50)(21,26,28,37,29,38,41,48,27,36,39,46,40,47,49,51);(21,27)(26,36)(28,39)(29,40)(37,46)(38,47)(41,49)(48,51)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4389);