Finite Group DatabasebetaFinite Group Databasebeta| order | 17738 |
| isoclinism | isoclinic class of D181 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D181 |
| unambiguous semidirect product | C181⋊(C2×C72) |
| Fitting, socle, Hall | C72×C181 ⋊ C2 |
| derived, Sylow | C181 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D181 |
| commutator, cosocle, hypocenter | C181 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C181 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8869 |
4508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#10624382, C7×C7⋊#10624382, C7×D7×D181, … |
| maximal normal subgroup of | C72×#10624382, C7×C7⋊#10624382, C7×D7×D181, … |
| maximal quotient of | C72×Dic181, C2×C72×D181 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17738, 10);