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C7×C13⋊C3×C41 #26014154

order11193
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C7×C41 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊C3×C41
unambiguous semidirect productC13⋊(C3×C7×C41)
unambiguous semidirect product(C13×C41)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C13×C41 ⋊ C3
derived, SylowC13 ⋊ C3×C7×C41
HallC13×C41 ⋊ C3×C7
HallC7×C13 ⋊ C3×C41

Subgroups

subgroupG/H
center, hypercenterC7×C41C13⋊C3
commutator, cosocle, hypocenterC13C3×C7×C41
FrattiniC1G
Fitting, socleC7×C13×C41C3
LCSG ▷ C13
UCSC1 ◁ C7×C41

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2009 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C13⋊C3×C41, C7×C13⋊C3×D41, C7×C41×D13⋊C3, …
maximal normal subgroup ofC2×C7×C13⋊C3×C41, C7×C13⋊C3×D41, C7×C41×D13⋊C3, …
maximal quotient ofC2×C7×C13⋊C3×C41, C7×C41×C13⋊C9, C3×C7×C13⋊C3×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11193, 2);