Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×H(5,𝔽2) ⋊ C22 |
| Sylow | C32 ⋊ C2×#577 |
3369 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=g,f^2=g,b^a=bf,f^a=fg,i^a=hi^2,f^b=fg,d^c=dg,h^e=h^2,i^e=i^2105 conjugacy classes — view the full character table.
| maximal subgroup of | #72214349, #72214885, #72214943 |
| maximal normal subgroup of | #72214349, #72214885, #72214943 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152876);