Finite Group DatabasebetaFinite Group Databasebeta| order | 17370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D193⋊C9) |
| unambiguous semidirect product | (C193⋊C9)⋊D5 |
| unambiguous semidirect product | D965⋊C9 |
| derived, Hall | C5×C193 ⋊ C2×C9 |
| Hall | C5×C193⋊C9 ⋊ C2 |
| Hall | D965 ⋊ C9 |
| Hall | C193⋊C9 ⋊ D5 |
| Sylow | C193 ⋊ C9×D5 |
| Sylow | C5 ⋊ D193⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D193⋊C3) |
| commutator, hypocenter | C5×C193 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C193 | C2×C3 |
| prime radical | C3×D965 | C3 |
| LCS | G ▷ C5×C193 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8685 |
Polycyclic presentation:
2,3,5,193,3|b^3=e,c^a=c^4,d^a=d^192,d^b=d^84516 conjugacy classes — view the full character table.
| maximal subgroup of | #16838801⋊C9, #16838802⋊C9, D5×D193⋊C9, … |
| maximal normal subgroup of | #16838801⋊C9, #16838802⋊C9, D5×D193⋊C9, … |
| maximal quotient of | Dic965⋊C9, C2×C5⋊(D193⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17370, 12);