Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #64188 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C24 |
| direct product | C2×#64188 |
| derived | C22⋊(C22⋊C9) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #64188 |
| commutator, cosocle, hypocenter | C22⋊(C22⋊C9) | C22 |
| Frattini | C3 | C2×#1020 |
| Fitting, socle | C25×C3 | D3 |
| LCS | G ▷ C22⋊(C22⋊C9) | |
| UCS | C1 ◁ C2 | |
449 conjugacy classes of subgroups; only the 25 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
36 conjugacy classes — view the full character table.
| maximal subgroup of | #64188⋊C4, #11919946, #11920036, … |
| maximal normal subgroup of | #64188⋊C4, #11919946, #11920036, … |
| maximal quotient of | #11921418, C4×#64188, C4⋊#64188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8263);