Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3 |
| direct product | Q8×#634 |
| Sylow | C32 ⋊ Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C3⋊D3 |
| commutator, socle, prime radical, cosocle | C22×C32 | C24 |
| Fitting | C32×C4×Q8 | C2 |
| hypercenter | C4×Q8 | C3⋊D3 |
| hypocenter | C32 | Q82 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
636 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | #11779041, #11779050, #11779058, … |
| maximal normal subgroup of | #11779041, #11779050, #11779058, … |
| maximal quotient of | Q8×#3750, C4⋊C4×#634, Q8×C4⋊(C3⋊Dic3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7919);