Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#157 |
| commutator, socle | C2×C32 | C22×C8 |
| Fitting | C32×M16 | C4 |
| prime radical | #3828 | C4 |
| cosocle | C3⋊(C3⋊C8) | C23 |
| hypercenter | M16 | #157 |
| hypocenter | C32 | #504 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ M16 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,c^2=e,d^2=e,e^2=f,g^a=gh,h^a=gh^2,c^b=cf,g^d=g^2,h^d=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11772726, #11797561, #11797563, … |
| maximal normal subgroup of | #11772726, #11797561, #11797563, … |
| maximal quotient of | #11795889, #11795890, #11796005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5654);