Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊#3861 |
| Fitting, socle, derived, Hall | C52×C72 ⋊ C2×C3 |
| Hall | C52⋊#3861 ⋊ C2 |
| Hall | C72×C5⋊D5 ⋊ C3 |
| Hall | C5⋊D5 ⋊ #3861 |
| Sylow | C72 ⋊ (C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C72 | C2×C3 |
| LCS | G ▷ C52×C72 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,7^2|c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^2,f^b=f^2234 conjugacy classes — view the full character table.
| maximal subgroup of | #28413357, #28413359, #1043⋊#3861, … |
| maximal normal subgroup of | #28413357, #28413359, #1043⋊#3861, … |
| maximal quotient of | #1039⋊#3861, C2×(C5⋊D5)⋊#3861, (C5⋊D5)⋊#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 119);