Finite Group Databasebeta

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C2×C3×D5×C169 #23778389

order10140
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C169 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D5×C169
unambiguous semidirect productC5⋊(C22×C3×C169)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C169)

Splittings

FittingC2×C3×C5×C169 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C169
HallC3×C5×C169 ⋊ C22
HallC5×C169 ⋊ C22×C3
HallC3×C5 ⋊ C22×C169

Subgroups

subgroupG/H
center, hypercenterC2×C3×C169D5
commutator, hypocenterC5C22×C3×C169
FrattiniC13C2×C3×D5×C13
FittingC2×C3×C5×C169C2
socleC2×C3×C5×C13C2×C13
prime radicalC2×C3×D5×C13C13
cosocleC5×C13C22×C3×C13
LCSG ▷ C5
UCSC1 ◁ C2×C3×C169

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4056 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D5×C169⋊C9, C2×C9×D5×C169, C2×C3×D5×C169⋊C3, …
maximal normal subgroup ofC2×D5×C169⋊C9, C2×C9×D5×C169, C2×C3×D5×C169⋊C3, …
maximal quotient ofC2×C9×D5×C169, C3×D3×D5×C169, C2×C3×D15×C169, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10140, 47);