Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C32×C42 ⋊ C22 |
| Sylow | C32 ⋊ #3018 |
1603 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^7,3^2|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,i^a=i^2,e^b=eg,f^b=fg,i^b=hi^2,e^c=eg,h^c=h^2,i^c=i^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72214293, #72214490, #72214505, … |
| maximal normal subgroup of | #72214293, #72214490, #72214505, … |
| maximal quotient of | C4×#10590397 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99010);