Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11234 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11389 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #391 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1446 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18,23,32)(15,25)(16,28)(17,20)(19,27)(21,29)(22,35,37,40)(24,39,38,31)(26,41)(30,43,33,36)(34,42);(12,14)(13,18,20,32)(15,22)(16,24)(17,23)(19,33,34,30)(21,31,28,39)(25,40,41,35)(26,37)(27,36)(29,38)(42,43);(12,15)(13,19,20,34)(14,22)(16,27)(17,26)(18,30,32,33)(21,25,28,41)(23,37)(24,36)(29,42)(31,35,39,40)(38,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4377);