Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61077 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#525 ◁ G | |
2762 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,27)(19,26)(20,24)(21,23)(22,25)(28,31)(29,30);(16,18)(17,20)(19,24)(21,30)(22,28)(23,27)(25,29)(26,31);(13,15)(16,19,22,21)(17,23,25,26)(18,24,28,30)(20,27,29,31);(16,20,22,29)(17,24,25,30)(18,23,28,26)(19,27,21,31);(17,25)(18,28)(23,26)(24,30)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54065);