Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19213 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,20)(14,21,19,16)(15,18,23,25)(22,27,26,24)(28,29)(30,36)(31,33)(32,40)(34,38)(35,39)(37,43)(41,42);(12,14,16,13,17,19,21,20)(15,22,24,18,23,26,27,25)(29,33)(34,42)(35,40)(36,43);(12,15)(13,18)(14,22)(16,24)(17,23)(19,26)(20,25)(21,27)(28,30,31,37)(29,34,33,42)(32,41,39,38)(35,43,40,36);(15,23)(18,25)(22,26)(24,27)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12201);