Finite Group Databasebeta

← Prev (#19153252) Next (#19153254) →

C22×C7×C41⋊C5 #19153253

order5740
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C7×C41⋊C5
unambiguous semidirect product(C22×C41)⋊(C5×C7)
unambiguous semidirect product(C22×C7×C41)⋊C5

Splittings

Fitting, socle, HallC22×C7×C41 ⋊ C5
derived, SylowC41 ⋊ C22×C5×C7
HallC7×C41 ⋊ C22×C5
HallC22×C41 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C7C41⋊C5
commutator, hypocenterC41C22×C5×C7
FrattiniC1G
Fitting, socleC22×C7×C41C5
LCSG ▷ C41
UCSC1 ◁ C22×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×ΓL(1,𝔽8)×C41⋊C5, C7×A4×C41⋊C5, C22⋊ΓL(1,𝔽8)×C41⋊C5, …
maximal normal subgroup ofC22×ΓL(1,𝔽8)×C41⋊C5, C7×A4×C41⋊C5, C22⋊ΓL(1,𝔽8)×C41⋊C5, …
maximal quotient ofC2×D3×C7×C41⋊C5, C22×C3×C7×C41⋊C5, C22×C7×C41⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 20);