Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×M16 ⋊ C22 |
| Sylow | C32 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D32 |
| commutator, socle | C2×C32 | C23×C4 |
| Fitting | C32×M16 | C22 |
| prime radical | D3×#235 | C2 |
| cosocle | C32×C4 | C24 |
| hypercenter | M16 | D32 |
| hypocenter | C32 | #568 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ M16 | |
547 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|d^2=e,e^2=f,d^a=df,h^a=h^2,c^b=cf,g^b=g^2,d^c=df84 conjugacy classes — view the full character table.
| maximal subgroup of | #11861153, #11861158, #11861180, … |
| maximal normal subgroup of | #11861153, #11861158, #11861180, … |
| maximal quotient of | #11857233, #11857239, #11857313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6588);