Finite Group DatabasebetaFinite Group Databasebeta| order | 2940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #64423⋊D5 |
| Fitting, socle, derived, Hall | C5×C72 ⋊ C22×C3 |
| Hall | D7×D35 ⋊ C3 |
| Hall | C5×#3861 ⋊ C22 |
| Hall | #3861 ⋊ C2×D5 |
| Sylow | C72 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ #64423⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72 | C22×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
Polycyclic presentation:
2^2,3,5,7^2|d^a=d^4,f^a=f^6,e^b=e^6,e^c=e^2,f^c=f^253 conjugacy classes — view the full character table.
| maximal subgroup of | #64423⋊D25, C5×#64423⋊D5, #64423⋊(C5⋊D5), … |
| maximal normal subgroup of | C5×#64423⋊D5, C11×#64423⋊D5, C13×#64423⋊D5, … |
| maximal quotient of | #64423⋊D25, C5×#64423⋊D5, #64423⋊(C5⋊D5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2940, 98);