Finite Group Databasebeta

← Prev (#22555330) Next (#22555332) →

C2×C3×C7×C29⋊C7 #22555331

order8526
isoclinismisoclinic class of C29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7

Aliases

direct productC2×C3×C7×C29⋊C7
unambiguous semidirect product(C2×C29)⋊(C3×C72)
unambiguous semidirect product(C2×C3×C29)⋊C72
unambiguous semidirect product(C2×C3×C7×C29)⋊C7

Splittings

Fitting, socleC2×C3×C7×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C3×C72
HallC2×C3×C29 ⋊ C72
HallC3×C29 ⋊ C2×C72
HallC2×C29 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C29⋊C7
commutator, hypocenterC29C2×C3×C72
FrattiniC1G
Fitting, socleC2×C3×C7×C29C7
LCSG ▷ C29
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×Dic29⋊C7, C3×C7⋊(Dic29⋊C7), C3×Dic7×C29⋊C7, …
maximal normal subgroup ofC3×C7×Dic29⋊C7, C3×C7⋊(Dic29⋊C7), C3×Dic7×C29⋊C7, …
maximal quotient ofC3×C4×C7×C29⋊C7, C22×C3×C7×C29⋊C7, C2×C7×C9×C29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8526, 29);