Finite Group DatabasebetaFinite Group Databasebeta| order | 2628 |
| isoclinism | isoclinic class of #14581496 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C73 ⋊ C4×C9 |
| Hall | #10620323 ⋊ C4 |
| Hall | #64408 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C73 | C4×C9 |
| prime radical, cosocle | D73⋊C3 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 73 |
Polycyclic presentation:
2,3,2,3,73|a^2=c,b^3=d,e^a=e^27,e^b=e^2,e^c=e^72,e^d=e^838 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14581496, #27190245, #27190246, … |
| maximal normal subgroup of | C5×#14581496, C7×#14581496, C11×#14581496, … |
| maximal quotient of | C5×#14581496, #27190245, #27190246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2628, 32);