Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#64139 |
| Fitting | C23×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×C3⋊D3 |
| commutator, cosocle | C22×C32 | C24 |
| Frattini | C22 | C23×C3⋊D3 |
| Fitting | C23×C32×C4 | C2 |
| socle | C23×C32 | C23 |
| hypercenter | C23×C4 | C3⋊D3 |
| hypocenter | C32 | C2×#121 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
1278 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 327 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11774074, #11774080, #11774090, … |
| maximal normal subgroup of | #11774074, #11774080, #11774090, … |
| maximal quotient of | C2×#10592911, C2×#10592912, C2×#10592639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8143);