Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#627 |
| Sylow | C32 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D32 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting, prime radical | C2×C32×D4 | C22 |
| hypercenter | C2×D4 | D32 |
| hypocenter | C32 | D4×Q8 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
607 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 607 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | #11779240, #11779650, #11780219, … |
| maximal normal subgroup of | #11779240, #11779650, #11780219, … |
| maximal quotient of | C22⋊C4×#627, D4×Dic3⋊Dic3, D4×#3724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7150);