Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of #11760384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C7 ⋊ C2×C3 |
| Hall | C7×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D35 ⋊ C3 |
| Hall | C52⋊C3 ⋊ D7 |
| Sylow | C52 ⋊ C3×D7 |
| Sylow | C7 ⋊ (C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
Polycyclic presentation:
2,3,5^2,7|c^a=c^4,d^a=d^4,e^a=e^6,c^b=cd,d^b=c^2d^343 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D7, D7×(C5⋊D5)⋊C3, C2×#11760384, … |
| maximal normal subgroup of | #3874⋊D7, D7×(C5⋊D5)⋊C3, C2×#11760384, … |
| maximal quotient of | #14523572, C2×#11760384, #15691245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 23);