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C3×C5×#10621721 #23778366

order10140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×#10621721

Splittings

Fitting, HallC3×C5×C169 ⋊ C4
derived, SylowC169 ⋊ C3×C4×C5
HallC5×C169 ⋊ C3×C4
HallC3×C169 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5#10621721
commutator, hypocenterC169C3×C4×C5
FrattiniC13C3×C5×#261
FittingC3×C5×C169C4
socleC3×C5×C13#261
prime radicalC3×C5×D169C2
cosocleD169C2×C3×C5
LCSG ▷ C169
UCSC1 ◁ C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

690 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#10621721⋊C9, C5×C9×#10621721, C3×C5×#10621721⋊C3, …
maximal normal subgroup ofC5×#10621721⋊C9, C5×C9×#10621721, C3×C5×#10621721⋊C3, …
maximal quotient ofC5×C9×#10621721, C32×C5×#10621721, C3×C5×C3⋊#10621721

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 24);