Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C32×D4 ⋊ D4 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
1798 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1798 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
Polycyclic presentation:
2^7,3^2|b^a=be,c^a=cf,i^a=hi^2,f^b=fg,e^c=eg,h^c=hi,i^c=i^2,h^d=h^2,i^d=i^2,h^f=h^2,i^f=i^263 conjugacy classes — view the full character table.
| maximal subgroup of | #72241543, #72252965, #72253195 |
| maximal normal subgroup of | #72241543, #72252965, #72253195 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99278);