Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C23×#3832 |
| Fitting | C23×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C23×C32×Q8 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C23×Q8 | C3⋊D3 |
| hypocenter | C32 | C23×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
19560 conjugacy classes of subgroups; only the 5001 normal subgroups are shown.
This group has 19560 conjugacy classes of subgroups — too many to draw. Only its 5001 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, 153204);