Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C32 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C8 | D32 |
| commutator, hypocenter | C32 | C4×C16 |
| Fitting, cosocle | C2×C32×C8 | C22 |
| socle, prime radical | C22×C32 | C2×C8 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C8 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=cd,c^2=e,e^2=f,h^a=h^2,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #11771542, #11771579, #11771597, … |
| maximal normal subgroup of | #11771542, #11771579, #11771597, … |
| maximal quotient of | #11771290, #11771314, #11772267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 984);