Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#63446 |
| Fitting | C2×C9×C22⋊C4 ⋊ C2 |
| Sylow | C9 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D9 |
| commutator, cosocle | C22×C9 | C24 |
| Frattini | C22×C3 | C23×D3 |
| Fitting | C2×C9×C22⋊C4 | C2 |
| socle | C23×C3 | C22×D3 |
| hypercenter | C2×C22⋊C4 | D9 |
| hypocenter | C9 | C2×#121 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
639 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #11774070, C4×#63446, #11802040, … |
| maximal normal subgroup of | #11774070, C4×#63446, #11802040, … |
| maximal quotient of | C2×#10588347, C2×#10588636, C2×#10588345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1473);