Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,24)(16,19)(17,23)(18,26)(21,25)(22,27);(12,13)(14,21,22,17)(15,18)(16,19)(20,23,27,25)(24,26);(12,14)(13,17)(15,25)(16,22)(18,27)(19,21)(20,24)(23,26);(15,26)(18,24)(20,27)(23,25)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16986);