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×#33373 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×Q8 | C24×C11 |
| prime radical | C11×#3498 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×Q8×C11 ◁ C2×C11×H(5,𝔽2) ◁ G | |
1312 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)(12,13,17,23,18,24,14,20)(15,21,26,19,16,22,25,27);(12,14,18,17)(13,19,24,27)(15,25,16,26)(20,22,23,21);(12,14,18,17)(13,20,24,23)(15,26,16,25)(19,22,27,21);(12,15,18,16)(13,21,24,22)(14,25,17,26)(19,20,27,23)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26361);