Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C3 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ Q8 |
| Sylow | C32 ⋊ #3501 |
1218 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|a^2=g,c^2=g,b^a=bf,c^a=cg,e^a=ef,h^a=hi,i^a=hi^2,d^b=df,h^c=i^2,i^c=h,h^g=h^2,i^g=i^254 conjugacy classes — view the full character table.
| maximal subgroup of | H(5,𝔽2)×PSU(3,𝔽2), #72222908, #72222912, … |
| maximal normal subgroup of | H(5,𝔽2)×PSU(3,𝔽2), #72222908, #72222912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 140258);