Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C2×#10594008 |
| Fitting | C2×C32×C42 ⋊ C22 |
| Sylow | C32 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C2×C32×C42 | C22 |
| socle | C23×C32 | C24 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | C22×#127 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
6249 conjugacy classes of subgroups; only the 820 normal subgroups are shown.
This group has 6249 conjugacy classes of subgroups — too many to draw. Only its 820 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D32×#127, #72243475, #72243765, … |
| maximal normal subgroup of | C2×D32×#127, #72243475, #72243765, … |
| maximal quotient of | #72243475 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134714);