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C13⋊C3×C5⋊D95 #49150304

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC13⋊C3×C5⋊D95
unambiguous semidirect productC5⋊(C13⋊C3×D95)

Splittings

Fitting, socle, derived, HallC52×C13×C19 ⋊ C2×C3
HallC52×C19×C13⋊C3 ⋊ C2
HallC13×C5⋊D95 ⋊ C3
HallC52×C13⋊C3 ⋊ D19
HallC19×C13⋊C3 ⋊ C5⋊D5
HallC52×C19 ⋊ C2×C13⋊C3
HallC52×C13 ⋊ C3×D19
HallC13×C19 ⋊ C3×C5⋊D5
SylowC52 ⋊ D19×C13⋊C3
SylowC19 ⋊ C13⋊C3×C5⋊D5
SylowC13 ⋊ C3×C5⋊D95

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C19C2×C3
LCSG ▷ C52×C13×C19
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6175

Conjugacy classes & character table

1673 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 130);