Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×C9×H(5,𝔽2) ⋊ C2 |
| Sylow | C9 ⋊ H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C25×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini, socle | C2×C3 | C25×D3 |
| Fitting | C2×C9×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | D9 |
| hypocenter | C9 | H(7,𝔽2) |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×H(5,𝔽2) | |
8988 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^7,3^2|h^3=i,b^a=bg,f^a=fg,e^b=eg,d^c=dg,h^f=h^2i^2,i^f=i^2201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153285);