Finite Group DatabasebetaFinite Group Databasebeta| order | 17602 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C677 · Schur multiplier (H2) = C1 |
| direct product | D13×C677 |
| unambiguous semidirect product | C13⋊(C2×C677) |
| Fitting, socle, Hall | C13×C677 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C677 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C677 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C677 |
| Frattini | C1 | G |
| Fitting, socle | C13×C677 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C677 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8801 |
5416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #261×C677, #47976182, D13×D677, … |
| maximal normal subgroup of | #261×C677, #47976182, D13×D677, … |
| maximal quotient of | Dic13×C677, C2×D13×C677 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17602, 3);