Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of (C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22×(C22⋊C9)⋊C4 |
| derived | C22⋊C9 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C22⋊C9)⋊C2 |
| commutator, hypocenter | C22⋊C9 | C22×C4 |
| Frattini | C2×C3 | C22×S4 |
| Fitting, socle, prime radical | C25×C3 | D3 |
| cosocle | C2×C22⋊C9 | C23 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C23 | |
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | (C22⋊C9)⋊#95, #11920191, #11920192, … |
| maximal normal subgroup of | (C22⋊C9)⋊#95, #11920191, #11920192, … |
| maximal quotient of | C22×(C22⋊C9)⋊C8, C2×#10589511, C2×C4×(C22⋊C9)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4985);