Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #10596770 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle | C24 ⋊ #157 |
| derived | A42 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | A42 | C4 |
| Fitting, socle | C24 | #157 |
| prime radical, cosocle | A4⋊S4 | C2 |
| LCS | G ▷ A42 | |
| UCS | C1 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 8 |
| transitive degree | μt(G) = 8 |
Polycyclic presentation:
2^2,3^2,2^4|a^2=b,c^a=cd,d^a=cd^2,e^a=g,f^a=h,g^a=f,h^a=e,c^b=c^2,d^b=d^2,e^b=f,f^b=e,g^b=h,h^b=g,e^c=ef,f^c=e,g^c=gh,h^c=g,e^d=ef,f^d=e13 conjugacy classes — view the full character table.
| maximal subgroup of | #10596770⋊C2, C2×#10596770, C3×#10596770, … |
| maximal normal subgroup of | #10596770⋊C2, C2×#10596770, C3×#10596770 |
| maximal quotient of | #11923440, #11923441, #11923442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8652);