Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×D72 |
| unambiguous semidirect product | (C7×D7)⋊(C22×C5) |
| unambiguous semidirect product | (C7⋊D7)⋊(C22×C5) |
| Fitting, socle | C2×C5×C72 ⋊ C22 |
| derived, Sylow | C72 ⋊ C23×C5 |
| Hall | C5×C72 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D72 |
| commutator, cosocle, hypocenter | C72 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C5 | |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×D72, C5×#11716115, #72243412, … |
| maximal normal subgroup of | C2×D5×D72, C5×#11716115, #72243412, … |
| maximal quotient of | C5×#11716115, D72×AGL(1,𝔽11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 134);