Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of #90866 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C13 ⋊ C4 |
| Sylow | C13 ⋊ #157 |
| Sylow | C32 ⋊ #261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13 | C4 |
| prime radical, cosocle | C3⋊D39 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 78 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2)(3,5,6,4)(8,9,10,12)(11,14,15,19)(13,17,18,16);(1,3,6)(2,5,4)(7,8,11,14,18,12,16,17,9,13,19,15,10)Polycyclic presentation:
2^2,3^2,13|a^2=b,c^a=cd^2,d^a=c^2d^2,e^a=e^8,c^b=c^2,d^b=d^2,e^b=e^1233 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊#157, C2×#90866, #90866⋊C3, … |
| maximal normal subgroup of | D13⋊#157, C2×#90866, #90866⋊C3, … |
| maximal quotient of | #11745509, C2×#90866, #13063979, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 41);