Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63964 |
| Sylow | C32 ⋊ C2×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D32 |
| commutator, cosocle | C22×C32 | C24 |
| Frattini | C22 | C22×D32 |
| Fitting, prime radical | C24×C32 | C22 |
| socle | C23×C32 | C23 |
| hypercenter | C24 | D32 |
| hypocenter | C32 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C24 | |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #11791846, #11791848, #11802270, … |
| maximal normal subgroup of | #11791846, #11791848, #11802270, … |
| maximal quotient of | C2×#10591716, C2×#10591718, C2×#10591693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7369);