Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of D35⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D35⋊D7 |
| unambiguous semidirect product | (C7⋊D7)⋊D5 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C22 |
| Sylow | C72 ⋊ C2×D5 |
| Sylow | C5 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
Polycyclic presentation:
2^2,5,7^2|c^a=c^4,d^a=d^6,d^b=d^6,e^b=e^677 conjugacy classes — view the full character table.
| maximal subgroup of | D72⋊D5, #5997⋊D5, D5×D72, … |
| maximal normal subgroup of | D72⋊D5, #5997⋊D5, D5×D72, … |
| maximal quotient of | #14519982, #14519983, #14519984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 28);