Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C2×C11×#3194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C24×C4×C11 ◁ G | |
2686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4)(5,9)(6,8)(7,10)(11,12)(13,16)(14,17)(15,18);(3,5)(4,7)(6,10)(8,9)(11,13,15,14)(12,16,18,17);(5,10)(7,9)(12,17)(13,14)(16,18);(4,8)(7,9)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53725);