Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×#10589567 |
| derived | H(3,𝔽4) ⋊ C2×C9 |
| Sylow | C2×H(3,𝔽4) ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C23×C3 | C22⋊A4 |
| commutator, hypocenter | H(3,𝔽4) | C2×C9 |
| Frattini | C22×C3 | C2×C22⋊A4 |
| Fitting, prime radical | C2×C3×H(3,𝔽4) | C3 |
| cosocle | C3×H(3,𝔽4) | C2×C3 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C23×C3 | |
621 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 621 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153850);