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C22×C5×C169⋊C3 #23778385

order10140
isoclinismisoclinic class of C169⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C169⋊C3

Splittings

Fitting, HallC22×C5×C169 ⋊ C3
derived, SylowC169 ⋊ C22×C3×C5
HallC5×C169 ⋊ C22×C3
HallC22×C169 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5C169⋊C3
commutator, cosocle, hypocenterC169C22×C3×C5
FrattiniC13C22×C5×C13⋊C3
FittingC22×C5×C169C3
socleC22×C5×C13C13⋊C3
LCSG ▷ C169
UCSC1 ◁ C22×C5

60 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×A4×C169⋊C3, C2×C5×D3×C169⋊C3, C22×C3×C5×C169⋊C3
maximal normal subgroup ofC5×A4×C169⋊C3, C22×C3×C5×C169⋊C3
maximal quotient ofC22×C5×C169⋊C9, C2×C5×D3×C169⋊C3, C22×C3×C5×C169⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 43);