Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#64223 |
| Sylow | C32 ⋊ C2×#135 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | GO+(4,𝔽2) |
| commutator, cosocle | C3⋊Dic3 | C24 |
| Frattini | C2 | C22×GO+(4,𝔽2) |
| Fitting | C2×C32×C4 | D4 |
| socle | C22×C32 | C2×D4 |
| hypocenter | C32 | C2×#135 |
| LCS | G ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 | |
430 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11787414, #11787415, #11791199, … |
| maximal normal subgroup of | #11787414, #11787415, #11791199, … |
| maximal quotient of | C2×#10593349, C2×#10593389, C2×C4×#3774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8378);