Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3932160 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C4 |
| abelian | C22×C4×C11×C16 |
| multiplicative | (ℤ/5865)ˣ, (ℤ/6256)ˣ, (ℤ/7360)ˣ, (ℤ/7820)ˣ, (ℤ/11730)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle, prime radical | C24×C11 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
1022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(25,26,27,28,29,30,31,32,33,34,35);(17,18,19,20);(21,22);(23,24)2816 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26308);