Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #11759813 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #92789 ⋊ C4 |
| Sylow | C132 ⋊ Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #11759813 |
| commutator, hypocenter | #92789 | C4 |
| Fitting, socle | C2×C132 | D3 |
| prime radical, cosocle | C2×#92789 | C2 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 52 |
Polycyclic presentation:
2,3,13^2,2|a^2=e,b^a=b^2,c^a=d,d^a=c,c^b=c^9,d^b=d^398 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523126, C7⋊#14523126, C11×#14523126, … |
| maximal normal subgroup of | C7×#14523126, C11×#14523126, C17×#14523126, … |
| maximal quotient of | C7×#14523126, C7⋊#14523126, C11×#14523126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 20);