Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C11 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C2×C11×#41 ◁ G | |
1134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,24)(15,20)(16,21)(17,22)(18,23)(19,26)(25,38)(27,39)(28,34)(29,43)(30,36)(31,37)(32,40)(33,42)(35,41);(12,14,18,27)(13,19,23,33)(15,25,16,29)(17,26,31,42)(20,32,21,35)(22,24,37,39)(28,40,30,41)(34,38,36,43);(12,15,18,16)(13,20,23,21)(14,25,27,29)(17,30,31,28)(19,32,33,35)(22,34,37,36)(24,38,39,43)(26,41,42,40);(12,16,18,15)(13,21,23,20)(14,25,27,29)(17,30,31,28)(19,32,33,35)(22,36,37,34)(24,38,39,43)(26,40,42,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26544);