Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×Q8 | C24×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×D4×C11 ◁ C2×C11×2−1+4 ◁ G | |
1176 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)(12,13,17,22,18,23,14,24)(15,20,29,36,27,34,25,38)(16,21,26,33,31,37,30,19)(28,35,39,42,40,43,41,32);(12,14,18,17)(13,19,23,33)(15,25,27,29)(16,30,31,26)(20,32,34,42)(21,22,37,24)(28,41,40,39)(35,36,43,38);(12,15)(13,20)(14,25)(16,28)(17,29)(18,27)(19,32)(21,35)(22,36)(23,34)(24,38)(26,39)(30,41)(31,40)(33,42)(37,43);(15,27)(20,34)(25,29)(28,40)(32,42)(35,43)(36,38)(39,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26360);