Finite Group DatabasebetaFinite Group Databasebeta| order | 588 |
| isoclinism | isoclinic class of #64418⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64418⋊C2 |
| Fitting, socle, Sylow | C72 ⋊ C2×D3 |
| derived, Hall | #3862 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #3862 | C22 |
| Fitting, socle | C72 | C2×D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14 |
Polycyclic presentation:
2^2,3,7^2|d^a=d^6,e^a=e^6,c^b=c^2,d^b=e^5,e^b=d^3,d^c=d^2,e^c=e^419 conjugacy classes — view the full character table.
| maximal subgroup of | #10596885⋊C2, C2×#64418⋊C2, (#64418⋊C2)⋊C3, … |
| maximal normal subgroup of | #10596885⋊C2, C2×#64418⋊C2, (#64418⋊C2)⋊C3, … |
| maximal quotient of | #11924161, #64418⋊C4, #11924163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(588, 35);