Finite Group DatabasebetaFinite Group Databasebeta| order | 17702 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | D53×C167 |
| unambiguous semidirect product | C53⋊(C2×C167) |
| Fitting, socle, Hall | C53×C167 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D53 |
| commutator, cosocle, hypocenter | C53 | C2×C167 |
| Frattini | C1 | G |
| Fitting, socle | C53×C167 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C167 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8851 |
4676 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C167×#6157, C167⋊#6157, D53×D167, … |
| maximal normal subgroup of | C167×#6157, C167⋊#6157, D53×D167, … |
| maximal quotient of | C167×Dic53, C2×D53×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17702, 1);