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C22×C7×C71⋊C5 #23755482

order9940
isoclinismisoclinic class of C71⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C7×C71⋊C5
unambiguous semidirect product(C22×C7×C71)⋊C5

Splittings

Fitting, socle, HallC22×C7×C71 ⋊ C5
derived, SylowC71 ⋊ C22×C5×C7
HallC7×C71 ⋊ C22×C5
HallC22×C71 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C7C71⋊C5
commutator, cosocle, hypocenterC71C22×C5×C7
FrattiniC1G
Fitting, socleC22×C7×C71C5
LCSG ▷ C71
UCSC1 ◁ C22×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×A4×C71⋊C5, C22⋊ΓL(1,𝔽8)×C71⋊C5, C22×ΓL(1,𝔽8)×C71⋊C5, …
maximal normal subgroup ofC7×A4×C71⋊C5, C22⋊ΓL(1,𝔽8)×C71⋊C5, C22×ΓL(1,𝔽8)×C71⋊C5, …
maximal quotient ofC2×D3×C7×C71⋊C5, C22×C3×C7×C71⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9940, 33);