Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | D9×H(3,𝔽4) |
| Fitting | C9×H(3,𝔽4) ⋊ C2 |
| Sylow | C9 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | C9×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D9 |
| hypocenter | C9 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
2112 conjugacy classes of subgroups; only the 530 normal subgroups are shown.
This group has 2112 conjugacy classes of subgroups — too many to draw. Only its 530 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, 144212);