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C7×Dic41⋊C5 #19153243

order5740
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic41⋊C5
unambiguous semidirect productDic41⋊(C5×C7)
unambiguous semidirect product(C7×Dic41)⋊C5

Splittings

derived, SylowC41 ⋊ C4×C5×C7
HallC7×C41⋊C5 ⋊ C4
HallC7×Dic41 ⋊ C5
HallC7×C41 ⋊ C4×C5
HallC41⋊C5 ⋊ C4×C7
HallDic41 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D41⋊C5
commutator, hypocenterC41C4×C5×C7
FrattiniC2C7×D41⋊C5
Fitting, socleC2×C7×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C7×Dic41⋊C5, C7×C3⋊(Dic41⋊C5), ΓL(1,𝔽8)×Dic41⋊C5, …
maximal normal subgroup ofC3×C7×Dic41⋊C5, ΓL(1,𝔽8)×Dic41⋊C5, C5×C7×Dic41⋊C5
maximal quotient ofC3×C7×Dic41⋊C5, C7×C3⋊(Dic41⋊C5), C7×Dic41⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 10);