Finite Group DatabasebetaFinite Group Databasebeta| order | 17914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | C2×C53⋊C169 |
| unambiguous semidirect product | (C2×C53)⋊C169 |
| derived, Sylow | C53 ⋊ C2×C169 |
| Hall | C2×C53 ⋊ C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C53⋊C13 |
| commutator, hypocenter | C53 | C2×C169 |
| Frattini | C13 | C2×C53⋊C13 |
| Fitting, socle, prime radical | C2×C13×C53 | C13 |
| cosocle | C13×C53 | C2×C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C13 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17914 |
442 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic53⋊C169, C4×C53⋊C169, C2×D53⋊C169, … |
| maximal normal subgroup of | Dic53⋊C169, C4×C53⋊C169, C2×D53⋊C169, … |
| maximal quotient of | C4×C53⋊C169, C22×C53⋊C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17914, 3);