Finite Group DatabasebetaFinite Group Databasebeta| order | 468 |
| isoclinism | isoclinic class of #90865 |
| 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 ⋊ Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13 | C4 |
| prime radical, cosocle | C13×C3⋊D3 | 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)(3,4,6,5)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19);(1,3,6)(7,8,10,12,14,16,18,19,17,15,13,11,9)Polycyclic presentation:
2^2,3^2,13|a^2=b,c^a=c^2d,d^a=cd,e^a=e^12,c^b=c^2,d^b=d^242 conjugacy classes — view the full character table.
| maximal subgroup of | #11745583, D13×#157, D32⋊D13, … |
| maximal normal subgroup of | #11745583, D13×#157, D32⋊D13, … |
| maximal quotient of | #11745508, C2×#90865, #13063978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(468, 40);