Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | #95×Dic9 |
| Sylow | C9 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D9 |
| commutator | C2×C9 | C43 |
| Frattini, socle, prime radical | C24×C3 | C22×D3 |
| Fitting | C2×C9×#95 | C2 |
| cosocle | C24×C9 | C23 |
| hypercenter | C2×#95 | D9 |
| hypocenter | C9 | C4×#95 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
1128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7148);