Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #14523148 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C132 ⋊ C3×C4 |
| Hall | #10621730 ⋊ C3 |
| Hall | #92788 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132 | C3×C4 |
| prime radical | #11759817 | C2 |
| cosocle | C13×D13 | C2×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 52 |
Polycyclic presentation:
2,3,2,13^2|a^2=c,d^a=d^5,e^a=e^12,d^b=d^3,e^b=e^3,d^c=d^1229 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523148, #28382288, #28382289, … |
| maximal normal subgroup of | C7×#14523148, C11×#14523148, C17×#14523148, … |
| maximal quotient of | C7×#14523148, #28382288, #28382289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 42);