Finite Group Databasebeta

← Prev (#28382574) Next (#28382576) →

C2×C5×C7×C29⋊C7 #28382575

order14210
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC2×C5×C7×C29⋊C7
unambiguous semidirect product(C2×C29)⋊(C5×C72)
unambiguous semidirect product(C2×C5×C29)⋊C72
unambiguous semidirect product(C2×C7×C29)⋊(C5×C7)
unambiguous semidirect product(C2×C5×C7×C29)⋊C7

Splittings

Fitting, socleC2×C5×C7×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C5×C72
HallC2×C5×C29 ⋊ C72
HallC5×C29 ⋊ C2×C72
HallC2×C29 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C29⋊C7
commutator, cosocle, hypocenterC29C2×C5×C72
FrattiniC1G
Fitting, socleC2×C5×C7×C29C7
LCSG ▷ C29
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2030

Conjugacy classes & character table

770 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×Dic29⋊C7, C5×C7⋊(Dic29⋊C7), C5×Dic7×C29⋊C7, …
maximal normal subgroup ofC5×C7×Dic29⋊C7, C5×C7⋊(Dic29⋊C7), C5×Dic7×C29⋊C7, …
maximal quotient ofC4×C5×C7×C29⋊C7, C22×C5×C7×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14210, 21);