Finite Group DatabasebetaFinite Group Databasebeta| order | 17602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D677⋊C13 |
| unambiguous semidirect product | (C677⋊C13)⋊C2 |
| Fitting, socle, derived, Sylow | C677 ⋊ C2×C13 |
| Hall | C677⋊C13 ⋊ C2 |
| Hall | D677 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C677 | C2×C13 |
| LCS | G ▷ C677 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 677 |
Polycyclic presentation:
2,13,677|c^a=c^676,c^b=c^36252 conjugacy classes — view the full character table.
| maximal subgroup of | #14582142⋊C13, C2×D677⋊C13 |
| maximal normal subgroup of | #14582142⋊C13, C2×D677⋊C13 |
| maximal quotient of | Dic677⋊C13, C2×D677⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17602, 1);