Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#73861 |
| Fitting | C32×#379 ⋊ C2 |
| Sylow | C32 ⋊ #2846 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C23×D3 |
| commutator, cosocle | C23×C3 | C24×C3 |
| Frattini | C23 | C23×C3×D3 |
| Fitting | C32×#379 | C2 |
| socle | C23×C32 | C24 |
| hypercenter | C3×#379 | D3 |
| hypocenter | C3 | C3×#2846 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23×C3 ◁ C3×#379 | |
7097 conjugacy classes of subgroups; only the 490 normal subgroups are shown.
This group has 7097 conjugacy classes of subgroups — too many to draw. Only its 490 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 90173);