Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C26×C3 |
| direct product | C3×#87537 |
| Fitting | C3×2−1+6 ⋊ C3 |
| Sylow | 2−1+6 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C24×A4 |
| commutator, cosocle, hypocenter | Q8 | C24×C32 |
| Frattini | C2 | C24×C3×A4 |
| Fitting | C3×2−1+6 | C3 |
| hypercenter | C3×H(5,𝔽2) | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C3×H(5,𝔽2) | |
2732 conjugacy classes of subgroups; only the 538 normal subgroups are shown.
This group has 2732 conjugacy classes of subgroups — too many to draw. Only its 538 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
201 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153895);