Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×#622 |
| derived, Sylow | C32 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #157 |
| commutator, hypocenter | C32 | C23×C8 |
| Frattini | C2 | C23×#157 |
| Fitting, socle, prime radical | C24×C32 | C4 |
| cosocle | C3⋊Dic3 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24 | |
574 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590207, #11783108, C2×#10590075, … |
| maximal normal subgroup of | C2×#10590207, #11783108, C2×#10590075, … |
| maximal quotient of | C22×C4×#622, C22×C22⋊#622, C22×C4⋊#622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8533);