Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C22×#63923 |
| Fitting | C23×C32×C4 ⋊ C22 |
| Sylow | C32 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D32 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C23×D32 |
| Fitting | C23×C32×C4 | C22 |
| socle | C24×C32 | C23 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | C22×#120 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
9769 conjugacy classes of subgroups; only the 972 normal subgroups are shown.
This group has 9769 conjugacy classes of subgroups — too many to draw. Only its 972 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134272);