Finite Group Databasebeta

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C13⋊C3×C79⋊C3 #22604460

order9243
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3

Aliases

direct productC13⋊C3×C79⋊C3
unambiguous semidirect product(C13⋊C3×C79)⋊C3
unambiguous semidirect product(C13×C79⋊C3)⋊C3
unambiguous semidirect product#15690493⋊C3
unambiguous semidirect product#15690494⋊C3

Splittings

Fitting, socle, derived, HallC13×C79 ⋊ C32
SylowC79 ⋊ C3×C13⋊C3
SylowC13 ⋊ C3×C79⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C79C32
LCSG ▷ C13×C79
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C13⋊C3)⋊(D79⋊C3), D13⋊C3×C79⋊C3, C13⋊C3×D79⋊C3, …
maximal normal subgroup of(C13⋊C3)⋊(D79⋊C3), D13⋊C3×C79⋊C3, C13⋊C3×D79⋊C3, …
maximal quotient ofC2×C13⋊C3×C79⋊C3, C22⋊(C13⋊C3)×C79⋊C3, C13⋊C3×C22⋊(C79⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9243, 11);