Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×#3699 |
| Fitting | C23×D4×C9 ⋊ C2 |
| Sylow | C9 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini | C2×C3 | C25×D3 |
| Fitting | C23×D4×C9 | C2 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C23×D4 | D9 |
| hypocenter | C9 | C23×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
9780 conjugacy classes of subgroups; only the 3726 normal subgroups are shown.
This group has 9780 conjugacy classes of subgroups — too many to draw. Only its 3726 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153197);