Finite Group Databasebeta

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C13⋊C3×C73⋊C3 #22555441

order8541
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×C73⋊C3
unambiguous semidirect product(C13⋊C3×C73)⋊C3
unambiguous semidirect product(C13×C73⋊C3)⋊C3
unambiguous semidirect product#15667864⋊C3
unambiguous semidirect product#15667865⋊C3

Splittings

Fitting, socle, derived, HallC13×C73 ⋊ C32
SylowC73 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C73⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C73C32
LCSG ▷ C13×C73
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8541, 10);