Finite Group DatabasebetaFinite Group Databasebeta| order | 2028 |
| isoclinism | isoclinic class of #14523161 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, Sylow | C132 ⋊ Dic3 |
| derived, Hall | #92789 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #92789 | C4 |
| Fitting, socle | C132 | Dic3 |
| prime radical, cosocle | #11759816 | C2 |
| LCS | G ▷ #92789 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 26 |
Polycyclic presentation:
2^2,3,13^2|a^2=b,c^a=c^2,d^a=d^4e^9,e^a=de^9,d^b=d^12,e^b=e^12,d^c=d^3e^11,e^c=e^920 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523161, C7⋊#14523161, C11×#14523161, … |
| maximal normal subgroup of | C7×#14523161, C11×#14523161, C17×#14523161, … |
| maximal quotient of | C7×#14523161, C7⋊#14523161, C11×#14523161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 55);