Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C3⋊C82 |
| derived, Sylow | C32 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C42 | D32 |
| commutator, hypocenter | C32 | C82 |
| Fitting, cosocle | C32×C42 | C22 |
| socle, prime radical | C22×C32 | C42 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C42 | |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #11771652, D3×C8×C3⋊C8, C8×#3710, … |
| maximal normal subgroup of | #11771652, D3×C8×C3⋊C8, C8×#3710, … |
| maximal quotient of | #11770700, C3⋊C8×C3⋊C16, #11771290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 959);