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C4×C13⋊C3×C41 #20264161

order6396
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×C41
unambiguous semidirect product(C4×C13)⋊(C3×C41)
unambiguous semidirect product(C4×C13×C41)⋊C3

Splittings

Fitting, HallC4×C13×C41 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C41
HallC13×C41 ⋊ C3×C4
HallC4×C13 ⋊ C3×C41

Subgroups

subgroupG/H
center, hypercenterC4×C41C13⋊C3
commutator, hypocenterC13C3×C4×C41
FrattiniC2C2×C13⋊C3×C41
FittingC4×C13×C41C3
socleC2×C13×C41C2×C3
LCSG ▷ C13
UCSC1 ◁ C4×C41

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic3×C13⋊C3×C41, C3×C4×C13⋊C3×C41, C4×C5×C13⋊C3×C41, …
maximal normal subgroup ofC3×C4×C13⋊C3×C41, C4×C5×C13⋊C3×C41, C4×C13⋊C3×C41⋊C5
maximal quotient ofC4×C41×C13⋊C9, Dic3×C13⋊C3×C41, C3×C4×C13⋊C3×C41, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6396, 2);