Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #5450 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C24 ⋊ C22×C9 |
| Sylow | H(3,𝔽4) ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #5450 |
| commutator, hypocenter | C24 | C22×C9 |
| Frattini, socle | C22×C3 | C22×A4 |
| Fitting, prime radical | C3×H(3,𝔽4) | C3 |
| cosocle | C24×C3 | C22×C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3^2,2^4|c^3=d,e^a=eh,f^a=fgh,e^b=eg,f^b=fh,e^c=ef,f^c=e,g^c=gh,h^c=g51 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10589552, #10588305⋊C2, #5450⋊C9, … |
| maximal normal subgroup of | C2×#10589552, #10588305⋊C2, #5450⋊C9, … |
| maximal quotient of | #2375⋊C9, #2785⋊C9, #11919477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1434);