Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C23×D32 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Frattini | C2 | C24×D32 |
| Fitting | C2×C32×#41 | C22 |
| hypercenter | C2×#41 | D32 |
| hypocenter | C32 | C2×#585 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
12357 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|e^2=g,b^a=bg,d^a=dg,c^b=cg,i^d=hi^2,h^f=h^2,i^f=i^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #72213893, #72214349, #72214664, … |
| maximal normal subgroup of | #72213893, #72214349, #72214664, … |
| maximal quotient of | C4×#10596675 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153275);