Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19621 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#19640 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3169 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
742 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)(14,21)(15,20)(16,25)(17,19)(18,22)(23,27)(24,26)(28,29)(30,36)(31,33)(32,40)(34,39)(35,37)(38,42)(41,43);(12,14,16,22,17,23,15,24)(13,18,20,21,19,26,25,27)(29,33)(34,41)(35,40)(36,42);(13,19)(18,26)(20,25)(21,27)(28,30,37,43,31,38,32,39)(29,34,40,42,33,41,35,36);(12,15,17,16)(13,20,19,25)(14,22,23,24)(18,27,26,21)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12628);