Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D36 |
| Fitting | C23×C4×C9 ⋊ C2 |
| Sylow | C9 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D9 |
| commutator, cosocle | C2×C9 | C25 |
| Frattini | C2×C3 | C24×D3 |
| Fitting | C23×C4×C9 | C2 |
| socle | C24×C3 | C2×D3 |
| hypercenter | C23×C4 | D9 |
| hypocenter | C9 | C23×D4 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
2043 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11773274, #11784633, #11784697, … |
| maximal normal subgroup of | #11773274, #11784633, #11784697, … |
| maximal quotient of | C23×(C2×D9)⋊C4, C23×C4⋊Dic9, C22×C4×D36, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5010);