Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #1020⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#1020⋊C2 |
| Fitting | C3×#120 ⋊ D3 |
| derived | C22⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #1020⋊C2 |
| commutator, cosocle, hypocenter | C22⋊A4 | C22×C3 |
| Frattini | C22 | C2×C3×S4 |
| Fitting | C3×#120 | D3 |
| socle | C22×C3 | C2×S4 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C3 | |
206 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | (#1020⋊C2)⋊D3, C3×#4625⋊C2, D3×#1020⋊C2, … |
| maximal normal subgroup of | (#1020⋊C2)⋊D3, C3×#4625⋊C2, D3×#1020⋊C2, … |
| maximal quotient of | C3×#72989, C3×#1020⋊C4, C3×#72991, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5464);