Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C32×C42 ⋊ C4 |
| Sylow | C32 ⋊ #382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#157 |
| commutator, socle | C22×C32 | C22×C4 |
| Fitting | C32×C42 | C4 |
| prime radical, cosocle | C22×C3⋊D3 | C23 |
| hypercenter | C42 | #157 |
| hypocenter | C32 | #382 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 | |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=e,c^2=f,b^a=bf,c^a=ce,g^a=gh,h^a=gh^2,g^d=g^2,h^d=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11770919, #11770920, #11770926, … |
| maximal normal subgroup of | #11770919, #11770920, #11770926, … |
| maximal quotient of | #11773184, #11773207, #11773394, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5618);