Finite Group DatabasebetaFinite Group Databasebeta| order | 2002 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D77 |
| unambiguous semidirect product | C7⋊(C13×D11) |
| unambiguous semidirect product | C11⋊(C13×D7) |
| Fitting, socle, Hall | C7×C11×C13 ⋊ C2 |
| derived, Hall | C7×C11 ⋊ C2×C13 |
| Hall | C11×C13 ⋊ D7 |
| Hall | C7×C13 ⋊ D11 |
| Sylow | C11 ⋊ C13×D7 |
| Sylow | C7 ⋊ C13×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C13 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1001 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31);(15,20)(16,19)(17,18)(22,31)(23,30)(24,29)(25,28)(26,27)520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D77, C13×D7×D11, D77⋊D13, … |
| maximal normal subgroup of | D13×D77, C13×D7×D11, D77⋊D13, … |
| maximal quotient of | C13×Dic77, C2×C13×D77, C13×D539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2002, 7);