Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C2×C11×#1599 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C23×D4×C11 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G | |
1372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(4,7)(5,9)(8,10)(15,18);(3,4,6,8)(5,10,9,7)(11,12)(13,15)(14,16)(17,18);(11,13,14,17)(12,15,16,18)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11098);