Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D5×D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D5×D72 |
| unambiguous semidirect product | (C7×D5×D7)⋊C2 |
| unambiguous semidirect product | (D5×C7⋊D7)⋊C2 |
| unambiguous semidirect product | (D7×D35)⋊C2 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C23 |
| Sylow | C72 ⋊ C22×D5 |
| Sylow | C5 ⋊ C2×D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72 | C23 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64423⋊C2, D72×AGL(1,𝔽5), #72225761, … |
| maximal normal subgroup of | D5×#64423⋊C2, D72×AGL(1,𝔽5), C2×D5×D72, … |
| maximal quotient of | #72225761, D5×#87639, C2×D5×D72, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 126);