Finite Group DatabasebetaFinite Group Databasebeta| order | 17450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D349 |
| unambiguous semidirect product | C349⋊(C2×C52) |
| Fitting, socle, Hall | C52×C349 ⋊ C2 |
| derived, Sylow | C349 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D349 |
| commutator, cosocle, hypocenter | C349 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C349 | C2 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8725 |
4400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#13063703, C5×#20296124, C5×D5×D349, … |
| maximal normal subgroup of | C52×#13063703, C5×#20296124, C5×D5×D349, … |
| maximal quotient of | C52×Dic349, C2×C52×D349 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17450, 10);