Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #14523151 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C132 ⋊ C3×C4 |
| Hall | #10621729 ⋊ C3 |
| Hall | C13×C13⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132 | C3×C4 |
| prime radical | (C13⋊C3)⋊D13 | C2 |
| cosocle | C13⋊D13 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2,3,2,13^2|a^2=c,d^a=d^5,e^a=e^8,d^b=d^3,d^c=d^12,e^c=e^1234 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523151, #28382294, #28382295, … |
| maximal normal subgroup of | C7×#14523151, C11×#14523151, C17×#14523151, … |
| maximal quotient of | C7×#14523151, #28382294, #28382295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 45);