Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C211 |
| direct product | C23×C11×#102 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C11 | D4 |
| commutator | C4 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C24×D4×C11 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C11 ◁ C24×C4×C11 ◁ G | |
7646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29);(3,4);(5,6);(7,8,9,10)(11,12)(13,15)(14,17)(16,18);(12,15)(13,18)(16,17)1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53065);