Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C24 |
| direct product | C4×C22⋊(C22⋊C9) |
| derived | C24 ⋊ C4×C9 |
| Sylow | C24×C4 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C22⋊A4 |
| commutator, hypocenter | C24 | C4×C9 |
| Frattini | C2×C3 | C2×C22⋊A4 |
| Fitting | C24×C3×C4 | C3 |
| socle, prime radical, cosocle | C25×C3 | C2×C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C4 | |
503 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #1779⋊C9, C4×#120⋊C9, C4⋊(#120⋊C9), … |
| maximal normal subgroup of | #1779⋊C9, C4×#120⋊C9, C4⋊(#120⋊C9), … |
| maximal quotient of | C4×C22⋊(Q8⋊C9), C4×#63703, C8×C22⋊(C22⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5003);