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C4×C5×C169⋊C3 #23778347

order10140
isoclinismisoclinic class of C169⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C169⋊C3
unambiguous semidirect product(C4×C169)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C169)⋊C3

Splittings

Fitting, HallC4×C5×C169 ⋊ C3
derived, SylowC169 ⋊ C3×C4×C5
HallC5×C169 ⋊ C3×C4
HallC4×C169 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C169⋊C3
commutator, hypocenterC169C3×C4×C5
FrattiniC2×C13C2×C5×C13⋊C3
FittingC4×C5×C169C3
socleC2×C5×C13C2×C13⋊C3
prime radicalC2×C5×C169⋊C3C2
cosocleC2×C169C2×C3×C5
LCSG ▷ C169
UCSC1 ◁ C4×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1180 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×Dic3×C169⋊C3, C3×C4×C5×C169⋊C3
maximal normal subgroup ofC3×C4×C5×C169⋊C3
maximal quotient ofC4×C5×C169⋊C9, C5×Dic3×C169⋊C3, C3×C4×C5×C169⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 5);