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×#61074 |
| 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 | |
2774 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)(16,17,22,26)(18,28,29,30)(19,27,21,24)(20,25,23,31);(16,18)(17,23)(19,25)(20,26)(21,31)(22,29)(24,28)(27,30);(13,15)(16,19,22,21)(17,24,26,27)(18,25,29,31)(20,30,23,28);(16,20)(17,25)(18,27)(19,30)(21,28)(22,23)(24,29)(26,31);(17,26)(18,29)(24,27)(25,31)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54062);