Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C22×C32×D4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#535 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C22×C32×D4 | C22 |
| hypercenter | C22×D4 | D32 |
| hypocenter | C32 | C2×#535 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
4473 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|b^2=f,b^a=bf,c^a=cg,d^a=df,i^a=hi^2,c^b=cf,h^e=h^2,i^e=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #72214414, #72214624, #72214786, … |
| maximal normal subgroup of | #72214414, #72214624, #72214786, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135026);