Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C3×C42 |
| direct product | C3⋊D3×H(3,𝔽4) |
| Fitting | C32×H(3,𝔽4) ⋊ C2 |
| Sylow | C32 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | C3⋊D3 |
| hypocenter | C32 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
4224 conjugacy classes of subgroups; only the 743 normal subgroups are shown.
This group has 4224 conjugacy classes of subgroups — too many to draw. Only its 743 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 144213);