Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×Dic32 |
| derived, Sylow | C32 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D32 |
| commutator, hypocenter | C32 | C22×C42 |
| Frattini | C22 | C22×D32 |
| Fitting, socle, prime radical | C24×C32 | C22 |
| cosocle | C22×C32 | C24 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24 | |
1114 conjugacy classes of subgroups; only the 552 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 552 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×C3⋊#95, #11773146, #11773185, … |
| maximal normal subgroup of | Dic3×C3⋊#95, #11773146, #11773185, … |
| maximal quotient of | C2×C4×Dic32, C22×#63579, C2×#10591222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7359);