Finite Group DatabasebetaFinite Group Databasebeta| order | 2628 |
| isoclinism | isoclinic class of #10620323⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C4×C9 |
| Hall | #10620323 ⋊ C4 |
| Hall | Dic73 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10620323⋊C2 |
| commutator, hypocenter | C73 | C4×C9 |
| Fitting, socle | C2×C73 | C2×C9 |
| prime radical, cosocle | C2×C73⋊C3 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 292 |
Polycyclic presentation:
2,3^2,73,2|a^2=e,b^3=c,d^a=d^72,d^b=d^4,d^c=d^6444 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14581484, #27190221, #27190247, … |
| maximal normal subgroup of | C5×#14581484, C7×#14581484, C11×#14581484, … |
| maximal quotient of | C5×#14581484, #27190221, #27190247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2628, 20);