Finite Group DatabasebetaFinite Group Databasebeta| order | 260 |
| isoclinism | isoclinic class of #63118 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C13 ⋊ C4 |
| Sylow | C13 ⋊ Dic5 |
| Sylow | C5 ⋊ #261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13 | C4 |
| prime radical, cosocle | C5×D13 | 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)(5,8,9,10)(7,12,13,11)(15,16)(17,18);(1,2,5,10,12,3,7,13,6,11,8,9,4)(14,15,17,18,16)Polycyclic presentation:
2^2,5,13|a^2=b,c^a=c^4,d^a=d^5,d^b=d^1223 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#261, C2×#63118, #63118⋊C3, … |
| maximal normal subgroup of | D5×#261, C2×#63118, #63118⋊C3, … |
| maximal quotient of | #10587062, C2×#63118, C3×#63118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(260, 6);