Finite Group Databasebeta

← Prev (#22555444) Next (#22555446) →

C3×C13×C73⋊C3 #22555445

order8541
isoclinismisoclinic class of C73⋊C3
automorphism?
homologyAbelianization (H1) = C32×C13 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13×C73⋊C3
unambiguous semidirect productC73⋊(C32×C13)
unambiguous semidirect product(C3×C73)⋊(C3×C13)

Splittings

Fitting, socleC3×C13×C73 ⋊ C3
derived, SylowC73 ⋊ C32×C13
HallC13×C73 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C13C73⋊C3
commutator, hypocenterC73C32×C13
FrattiniC1G
Fitting, socleC3×C13×C73C3
LCSG ▷ C73
UCSC1 ◁ C3×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1053 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C13×D73⋊C3, C3×(C73⋊C3)⋊D13, C3×D13×C73⋊C3, …
maximal normal subgroup ofC3×C13×D73⋊C3, C3×(C73⋊C3)⋊D13, C3×D13×C73⋊C3, …
maximal quotient ofC2×C3×C13×C73⋊C3, A4×C13×C73⋊C3, C3×C13×C22⋊(C73⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8541, 14);