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C3×#16809977 #23778371

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

Aliases

direct productC3×#16809977

Splittings

Fitting, HallC3×C5×C169 ⋊ C4
derived, HallC5×C169 ⋊ C3×C4
HallC3×C169 ⋊ Dic5
SylowC169 ⋊ C3×Dic5
HallC3×C5 ⋊ #10621721
SylowC5 ⋊ C3×#10621721

Subgroups

subgroupG/H
center, hypercenterC3#16809977
commutator, hypocenterC5×C169C3×C4
FrattiniC13C3×#63118
FittingC3×C5×C169C4
socleC3×C5×C13#261
prime radicalC3×C5×D169C2
cosocleC5×D169C2×C3
LCSG ▷ C5×C169
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

654 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#16809977⋊C9, C9×#16809977, C3×#16809977⋊C3, …
maximal normal subgroup of#16809977⋊C9, C9×#16809977, C3×#16809977⋊C3, …
maximal quotient ofC9×#16809977, C32×#16809977, C3×C3⋊#16809977

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 29);