Finite Group DatabasebetaFinite Group Databasebeta| order | 12740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C5×C7⋊D91 |
| unambiguous semidirect product | (C2×C7)⋊(C5×D91) |
| unambiguous semidirect product | (C2×C13)⋊(C5×C7⋊D7) |
| Fitting, socle | C2×C5×C72×C13 ⋊ C2 |
| derived, Hall | C72×C13 ⋊ C22×C5 |
| Hall | C5×C72×C13 ⋊ C22 |
| Hall | C5×C72 ⋊ C2×D13 |
| Hall | C5×C13 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×C5×D13 |
| Sylow | C13 ⋊ C2×C5×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C7⋊D91 |
| commutator, cosocle, hypocenter | C72×C13 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | C2 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C2×C5 | |
200 conjugacy classes of subgroups.
3200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12740, 106);