Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C11×#1287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #95 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C24×C11 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4,6,11,8,12,7,10)(5,13,14,9,16,17,15,18)(19,20)(21,27,29,33)(22,25)(23,26)(24,28,31,34)(30,32);(3,5,7,15,8,16,6,14)(4,9,11,17,12,18,10,13)(19,21)(20,24,26,31)(22,28)(23,29)(25,27,32,33)(30,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 951);