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D5×C13×D13⋊C3 #23778488

order10140
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productD5×C13×D13⋊C3
unambiguous semidirect productD13⋊(C3×D5×C13)
unambiguous semidirect product(D5×D13)⋊(C3×C13)
unambiguous semidirect product(C5×D13⋊C3)⋊(C2×C13)
unambiguous semidirect product(D5×C13⋊C3)⋊(C2×C13)
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C2×C13)

Splittings

Fitting, socle, HallC5×C132 ⋊ C22×C3
derivedC5×C13 ⋊ C22×C3×C13
HallD5×C13×D13 ⋊ C3
HallC5×C13×C13⋊C3 ⋊ C22
HallC13×C13⋊C3 ⋊ C2×D5
SylowC132 ⋊ C2×C3×D5
SylowC5 ⋊ C2×C13×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC13D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C3×C13
FrattiniC1G
Fitting, socleC5×C132C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C13

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C13⋊C3×D13⋊C3, C3×D5×C13×D13⋊C3, C13×D15×D13⋊C3, …
maximal normal subgroup ofD5×C13⋊C3×D13⋊C3, C3×D5×C13×D13⋊C3
maximal quotient ofD5×C13×D13⋊C9, C3×D5×C13×D13⋊C3, C13×D15×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 146);