Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C22×C32×Q8 ⋊ C2 |
| Sylow | C32 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C23 |
| Fitting | C22×C32×Q8 | C2 |
| prime radical | C23×C3⋊D3 | C22 |
| hypercenter | C22×Q8 | C3⋊D3 |
| hypocenter | C32 | #393 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
606 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=f,c^2=f,b^a=be,c^a=cd,g^a=g^2,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11771925, #11778203, #11778218, … |
| maximal normal subgroup of | #11771925, #11778203, #11778218, … |
| maximal quotient of | #11773291, #11773392, #11773482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4812);