Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C2×C32 |
| Hall | C52⋊C3×C31⋊C3 ⋊ C2 |
| Hall | C52×D31 ⋊ C32 |
| Hall | D31 ⋊ C3×C52⋊C3 |
| Sylow | C31 ⋊ C2×C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C31 | C2×C32 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
121 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D31⋊C3, (C5⋊D5)⋊C3×D31⋊C3, C2×C52⋊C3×D31⋊C3 |
| maximal normal subgroup of | #3874×D31⋊C3, (C5⋊D5)⋊C3×D31⋊C3, C2×C52⋊C3×D31⋊C3 |
| maximal quotient of | C52⋊C3×(C31⋊C3)⋊C4, C2×C52⋊C3×D31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 101);