Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D32×#41 |
| Fitting | C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D32 |
| commutator, socle, cosocle | C2×C32 | C25 |
| Frattini | C2 | C23×D32 |
| Fitting | C32×#41 | C22 |
| hypercenter | #41 | D32 |
| hypocenter | C32 | C22×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ #41 | |
1862 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #11784808, #11857481, D32×#104, … |
| maximal normal subgroup of | #11784808, #11857481, D32×#104, … |
| maximal quotient of | D32×#117, C4×D32×D4, C4×D32×Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8572);