Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#64241 |
| Fitting | C23×C32 ⋊ D4 |
| Sylow | C32 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×GO+(4,𝔽2) |
| commutator, cosocle | C2×C3⋊D3 | C24 |
| Frattini | C2 | C22×GO+(4,𝔽2) |
| Fitting | C23×C32 | D4 |
| socle | C22×C32 | C2×D4 |
| hypercenter | C23 | GO+(4,𝔽2) |
| hypocenter | C32 | C2×#120 |
| LCS | G ▷ C2×C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C23 | |
1154 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8418);