Finite Group DatabasebetaFinite Group Databasebeta| order | 1820 |
| isoclinism | isoclinic class of #63118 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#63118 |
| Fitting, socle, Hall | C5×C7×C13 ⋊ C4 |
| derived, Hall | C5×C13 ⋊ C4×C7 |
| Hall | C7×C13 ⋊ Dic5 |
| Hall | C5×C7 ⋊ #261 |
| Sylow | C13 ⋊ C7×Dic5 |
| Sylow | C5 ⋊ C7×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #63118 |
| commutator, hypocenter | C5×C13 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C13 | C4 |
| prime radical | C5×C7×D13 | C2 |
| cosocle | C5×D13 | C2×C7 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 455 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5,6,7)(9,10,11,13)(12,15,16,17)(14,19,20,18)(22,23)(24,25);(8,9,12,17,19,10,14,20,13,18,15,16,11)(21,22,24,25,23)161 conjugacy classes — view the full character table.
| maximal subgroup of | C49×#63118, C72×#63118, C7×C7⋊#63118, … |
| maximal normal subgroup of | C49×#63118, C72×#63118, C7×C11×#63118, … |
| maximal quotient of | C49×#63118, C72×#63118, C7×C7⋊#63118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1820, 19);