Finite Group DatabasebetaFinite Group Databasebeta| order | 1092 |
| isoclinism | isoclinic class of C7⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C7⋊#261 |
| Fitting, socle, Hall | C3×C7×C13 ⋊ C4 |
| derived, Hall | C7×C13 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ Dic7 |
| Hall | C3×C7 ⋊ #261 |
| Sylow | C13 ⋊ C3×Dic7 |
| Sylow | C7 ⋊ C3×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C7⋊#261 |
| commutator, hypocenter | C7×C13 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13 | C4 |
| prime radical | C3×C7×D13 | C2 |
| cosocle | C7×D13 | C2×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 273 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(5,6,7,9)(8,11,12,13)(10,15,16,14)(18,19)(20,21)(22,23);(4,5,8,13,15,6,10,16,9,14,11,12,7)(17,18,20,22,23,21,19)93 conjugacy classes — view the full character table.
| maximal subgroup of | #15692586, (C7⋊C9)⋊#261, #15692591, … |
| maximal normal subgroup of | #15692586, (C7⋊C9)⋊#261, #15692591, … |
| maximal quotient of | C9×C7⋊#261, C32×C7⋊#261, C3×C3⋊(C7⋊#261), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1092, 51);