Finite Group DatabasebetaFinite Group Databasebeta| order | 17542 |
| isoclinism | isoclinic class of D179 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D179 |
| unambiguous semidirect product | C179⋊(C2×C72) |
| Fitting, socle, Hall | C72×C179 ⋊ C2 |
| derived, Sylow | C179 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D179 |
| commutator, cosocle, hypocenter | C179 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C179 | C2 |
| LCS | G ▷ C179 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8771 |
4459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D179, C7⋊D7×D179, C2×C72×D179 |
| maximal normal subgroup of | C7×D7×D179, C7⋊D7×D179, C2×C72×D179 |
| maximal quotient of | C72×Dic179, C2×C72×D179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17542, 10);