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C5×Dic7×C41 #19153237

order5740
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic7×C41
unambiguous semidirect productC7⋊(C4×C5×C41)

Splittings

derived, SylowC7 ⋊ C4×C5×C41
HallC5×C7×C41 ⋊ C4
HallC7×C41 ⋊ C4×C5
HallC5×C7 ⋊ C4×C41

Subgroups

subgroupG/H
center, hypercenterC2×C5×C41D7
commutator, hypocenterC7C4×C5×C41
FrattiniC2C5×D7×C41
Fitting, socleC2×C5×C7×C41C2
LCSG ▷ C7
UCSC1 ◁ C2×C5×C41

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×Dic7×C41, C5×C41×Dic21, C5×C41×ΓL(1,𝔽8)⋊C4, …
maximal normal subgroup ofC3×C5×Dic7×C41, C5×C41×ΓL(1,𝔽8)⋊C4, C25×Dic7×C41, …
maximal quotient ofC3×C5×Dic7×C41, C5×C41×Dic21, C25×Dic7×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 4);