Finite Group Databasebeta

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C13⋊C3×D295 #37527666

order23010
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D295
unambiguous semidirect productC5⋊(C13⋊C3×D59)
unambiguous semidirect productC59⋊(D5×C13⋊C3)
unambiguous semidirect product(C13×D295)⋊C3

Splittings

Fitting, socle, derived, HallC5×C13×C59 ⋊ C2×C3
HallC5×C13⋊C3×C59 ⋊ C2
HallC13×D295 ⋊ C3
HallC13⋊C3×C59 ⋊ D5
HallC13×C59 ⋊ C3×D5
HallC5×C59 ⋊ C2×C13⋊C3
HallC5×C13⋊C3 ⋊ D59
HallC5×C13 ⋊ C3×D59
SylowC59 ⋊ D5×C13⋊C3
SylowC13 ⋊ C3×D295
SylowC5 ⋊ C13⋊C3×D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C13×C59C2×C3
LCSG ▷ C5×C13×C59
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3835

Conjugacy classes & character table

1043 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 22);