Finite Group DatabasebetaFinite Group Databasebeta| order | 17542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1253 |
| unambiguous semidirect product | C7⋊(C7×D179) |
| unambiguous semidirect product | C179⋊(C7×D7) |
| Fitting, socle, Hall | C72×C179 ⋊ C2 |
| derived | C7×C179 ⋊ C2×C7 |
| Sylow | C179 ⋊ C7×D7 |
| Sylow | C72 ⋊ D179 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1253 |
| commutator, cosocle, hypocenter | C7×C179 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C179 | C2 |
| LCS | G ▷ C7×C179 | |
| UCS | C1 ◁ C7 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2506 |
4396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D179, D7×D1253, (C7⋊D7)⋊D179, … |
| maximal normal subgroup of | C7×D7×D179, D7×D1253, (C7⋊D7)⋊D179, … |
| maximal quotient of | C7×Dic1253, C2×C7×D1253 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17542, 8);