Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#32698 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
594 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)(12,13,17,20,16,21,25,27)(14,18,19,26,22,15,23,24);(12,14)(13,18)(15,21)(16,22)(17,23)(19,25)(20,24)(26,27);(12,15)(13,19,21,23)(14,20,22,27)(16,18)(17,24)(25,26);(14,22)(17,25)(20,27)(24,26)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25686);