Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C7⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7 |
| direct product | AGL(1,𝔽5)×C7⋊D7 |
| unambiguous semidirect product | (C7×AGL(1,𝔽5))⋊D7 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C2×C4 |
| Sylow | C72 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C72 | C2×C4 |
| prime radical | D5×C7⋊D7 | C2 |
| cosocle | C72×D5 | C22 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 245 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#64424, D72×AGL(1,𝔽5), C7⋊D7×#1043, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#64424, D72×AGL(1,𝔽5), AGL(1,𝔽5)×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C7⋊D7×#1043, C2×AGL(1,𝔽5)×C7⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 116);