Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63983 |
| commutator, cosocle | C24×C32 | C23 |
| Frattini | C24 | C2×D32 |
| Fitting | C25×C32 | C22 |
| socle | C22×C32 | #120 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | #2021 |
| LCS | G ▷ C24×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C25 | |
1607 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^a=bd,c^a=ce,f^a=fg,h^a=h^2,i^a=i^2,c^b=cf,d^c=dg,i^c=hi^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #72252316, #72252346, #72252347 |
| maximal normal subgroup of | #72252316, #72252346, #72252347 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 26814);