Finite Group DatabasebetaFinite Group Databasebeta| order | 2132 |
| isoclinism | isoclinic class of #14523822 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C41 ⋊ C4 |
| Sylow | C41 ⋊ #261 |
| Sylow | C13 ⋊ #4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C41 | C4 |
| prime radical, cosocle | D533 | C2 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 54 |
| transitive degree | μt(G) = 533 |
Polycyclic presentation:
2^2,13,41|a^2=b,c^a=c^5,d^a=d^9,c^b=c^12,d^b=d^40137 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14523822, C7⋊#14523822, #34062995, … |
| maximal normal subgroup of | C7×#14523822, C11×#14523822, C13×#14523822, … |
| maximal quotient of | C7×#14523822, C7⋊#14523822, #34062995, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2132, 9);