Finite Group DatabasebetaFinite Group Databasebeta| order | 14550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | D97⋊(C52⋊C3) |
| Fitting, socle, derived, Hall | C52×C97 ⋊ C2×C3 |
| Hall | C52⋊(C97⋊C3) ⋊ C2 |
| Hall | C52×D97 ⋊ C3 |
| Hall | D97 ⋊ C52⋊C3 |
| Sylow | C97 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ D97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C97 | C2×C3 |
| LCS | G ▷ C52×C97 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1455 |
Polycyclic presentation:
2,3,5^2,97|e^a=e^96,c^b=c^3d^2,d^b=cd,e^b=e^35422 conjugacy classes — view the full character table.
| maximal subgroup of | #87604⋊(C52⋊C3), #44414939, D97⋊((C5⋊D5)⋊C3), … |
| maximal normal subgroup of | #87604⋊(C52⋊C3), #44414939, D97⋊((C5⋊D5)⋊C3), … |
| maximal quotient of | Dic97⋊(C52⋊C3), C2×D97⋊(C52⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14550, 25);