Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#624 |
| derived, Sylow | C32 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D32 |
| commutator, hypocenter | C32 | C24×C4 |
| Frattini | C2 | C23×D32 |
| Fitting, socle | C24×C32 | C22 |
| prime radical | C24×C3⋊D3 | C2 |
| cosocle | C2×C32 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24 | |
3098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #11773162, #11773168, C2×#10591370, … |
| maximal normal subgroup of | #11773162, #11773168, C2×#10591370, … |
| maximal quotient of | C22×C4×#624, C23×Dic32, C22×#63974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8584);