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C5×C3⋊#10621721 #23778372

order10140
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#10621721
unambiguous semidirect productC3⋊(C5×#10621721)

Splittings

Fitting, HallC3×C5×C169 ⋊ C4
derived, HallC3×C169 ⋊ C4×C5
HallC5×C169 ⋊ Dic3
SylowC169 ⋊ C5×Dic3
HallC3×C5 ⋊ #10621721
SylowC3 ⋊ C5×#10621721

Subgroups

subgroupG/H
center, hypercenterC5C3⋊#10621721
commutator, hypocenterC3×C169C4×C5
FrattiniC13C5×C3⋊#261
FittingC3×C5×C169C4
socleC3×C5×C13#261
prime radicalC3×C5×D169C2
cosocleC3×D169C2×C5
LCSG ▷ C3×C169
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊#10621721, C5×C3⋊(#10621721⋊C3), C3×C5×C3⋊#10621721, …
maximal normal subgroup ofC5×C3⋊(#10621721⋊C3), C3×C5×C3⋊#10621721
maximal quotient ofC5×C9⋊#10621721, C3×C5×C3⋊#10621721, C5×C3⋊(C3⋊#10621721)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 30);