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C2×C11×D29⋊C7 #22582004

order8932
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D29⋊C7
unambiguous semidirect productD29⋊(C2×C7×C11)
unambiguous semidirect product(C2×D29)⋊(C7×C11)
unambiguous semidirect product(C29⋊C7)⋊(C22×C11)
unambiguous semidirect product(C2×C29⋊C7)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D29)⋊C7

Splittings

Fitting, socleC2×C11×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C22×C7×C11
HallC11×C29⋊C7 ⋊ C22
HallC2×C11×D29 ⋊ C7
HallC11×C29 ⋊ C22×C7
HallC29⋊C7 ⋊ C22×C11
HallC2×D29 ⋊ C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D29⋊C7
commutator, hypocenterC29C22×C7×C11
FrattiniC1G
Fitting, socleC2×C11×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C11×D29⋊C7, C2×C3×C11×D29⋊C7, C2×C11×C3⋊(D29⋊C7)
maximal normal subgroup ofC2×C3×C11×D29⋊C7
maximal quotient ofD3×C11×D29⋊C7, C2×C3×C11×D29⋊C7, C2×C11×C3⋊(D29⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8932, 17);