Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63829 |
| Sylow | C32 ⋊ C2×#135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #626 |
| commutator, cosocle | C32×C4 | C24 |
| Frattini | C4 | C22×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle | C22×C32 | C2×D4 |
| hypercenter | C22×C4 | D32 |
| hypocenter | C32 | C2×#135 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
614 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11787390, #11787391, #11787393, … |
| maximal normal subgroup of | #11787390, #11787391, #11787393, … |
| maximal quotient of | C2×#10591084, C2×#10591105, C2×#10591122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6674);