Finite Group DatabasebetaFinite Group Databasebeta| order | 8330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C5⋊(C7⋊D119) |
| unambiguous semidirect product | C7⋊D595 |
| unambiguous semidirect product | C17⋊(C5⋊(C7⋊D7)) |
| Fitting, socle, derived, Hall | C5×C72×C17 ⋊ C2 |
| Hall | C72×C17 ⋊ D5 |
| Hall | C5×C72 ⋊ D17 |
| Hall | C5×C17 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D85 |
| Sylow | C17 ⋊ C5⋊(C7⋊D7) |
| Sylow | C5 ⋊ C7⋊D119 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72×C17 | C2 |
| LCS | G ▷ C5×C72×C17 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,7^2,17|b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^162084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30659441, #30659442, D17×C5⋊(C7⋊D7), … |
| maximal normal subgroup of | #30659441, #30659442, D17×C5⋊(C7⋊D7), … |
| maximal quotient of | C7⋊Dic595, C2×C5⋊(C7⋊D119), C3×C5⋊(C7⋊D119), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8330, 20);