Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #1020⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×#1020⋊C3 |
| unambiguous semidirect product | (C2×#1020)⋊C3 |
| Fitting, socle | C25 ⋊ C3×D3 |
| derived | C22⋊A4 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #1020⋊C3 |
| commutator, cosocle, hypocenter | C22⋊A4 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C25 | C3×D3 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C2 | |
149 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 149 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | (#1020⋊C3)⋊C4, #11923470, #11923471, … |
| maximal normal subgroup of | (#1020⋊C3)⋊C4, #11923470, #11923471, … |
| maximal quotient of | #87502⋊C3, C4×#1020⋊C3, C4⋊(#1020⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8656);