Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 196608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4 |
| abelian | C2×C32×C4×C16 |
| multiplicative | (ℤ/1547)ˣ, (ℤ/1989)ˣ, (ℤ/3094)ˣ, (ℤ/3978)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C8 | C23×C32 |
| socle, prime radical | C23×C32 | C2×C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1152 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(23,24,25);(17,18,19,20)(26,27,28);(21,22)1152 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3165);