Finite Group DatabasebetaFinite Group Databasebeta| order | 260 |
| isoclinism | isoclinic class of #63122 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C13 ⋊ C4 |
| Sylow | C13 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13 | C4 |
| prime radical, cosocle | D65 | C2 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 65 |
A minimal faithful permutation representation — 2 generators on 18 points:
(2,3,4,6)(5,8,9,13)(7,11,12,10)(15,16,17,18);(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,15,18,16,17)Polycyclic presentation:
2^2,5,13|a^2=b,c^a=c^3,d^a=d^8,c^b=c^4,d^b=d^1220 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#261, C2×#63122, #63122⋊C3, … |
| maximal normal subgroup of | D5⋊#261, C2×#63122, #63122⋊C3, … |
| maximal quotient of | #10587066, C2×#63122, C3×#63122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(260, 10);