Finite Group Databasebeta

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C13⋊C3×C67⋊C3 #21463206

order7839
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×C67⋊C3
unambiguous semidirect product(C13⋊C3×C67)⋊C3
unambiguous semidirect product(C13×C67⋊C3)⋊C3
unambiguous semidirect product#14579731⋊C3
unambiguous semidirect product#14579732⋊C3

Splittings

Fitting, socle, derived, HallC13×C67 ⋊ C32
SylowC67 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C67⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C67C32
LCSG ▷ C13×C67
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C13⋊C3)⋊(D67⋊C3), D13⋊C3×C67⋊C3, C13⋊C3×D67⋊C3, …
maximal normal subgroup of(C13⋊C3)⋊(D67⋊C3), D13⋊C3×C67⋊C3, C13⋊C3×D67⋊C3, …
maximal quotient ofC2×C13⋊C3×C67⋊C3, C22⋊(C13⋊C3)×C67⋊C3, C13⋊C3×C22⋊(C67⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7839, 7);