Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #672 |
| Fitting | C24×C32 ⋊ C22 |
| Sylow | C32 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C24×C32 | C22 |
| hypercenter | C24 | D32 |
| hypocenter | C32 | D42 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C24 | |
921 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 921 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | #11798540, #11902326, D3×D4×#67, … |
| maximal normal subgroup of | #11798540, #11902326, D3×D4×#67, … |
| maximal quotient of | #67×(C2×D3)⋊C4, #67×#217, #67×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7407);