Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24402 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,22,24,21,19,20,30)(18,25,29,26,28,23,27,31);(13,15)(16,18)(17,23)(19,25)(20,27)(21,28)(22,29)(24,31)(26,30);(16,19)(17,21)(18,26)(20,30)(22,24)(23,27)(25,29)(28,31);(13,15)(16,20,21,22)(17,24,19,30)(18,27,28,29)(23,31,25,26)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17390);