Finite Group Databasebeta

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C2×D35×C169 #37556804

order23660
automorphism?
homologyAbelianization (H1) = C22×C169 · Schur multiplier (H2) = C2

Aliases

direct productC2×D35×C169
unambiguous semidirect product(C2×C5)⋊(D7×C169)
unambiguous semidirect product(C2×C7)⋊(D5×C169)

Splittings

FittingC2×C5×C7×C169 ⋊ C2
derived, HallC5×C7 ⋊ C22×C169
HallC5×C7×C169 ⋊ C22
HallC7×C169 ⋊ C2×D5
HallC5×C169 ⋊ C2×D7
SylowC7 ⋊ C2×D5×C169
SylowC5 ⋊ C2×D7×C169

Subgroups

subgroupG/H
center, hypercenterC2×C169D35
commutator, hypocenterC5×C7C22×C169
FrattiniC13C2×C13×D35
FittingC2×C5×C7×C169C2
socleC2×C5×C7×C13C2×C13
prime radicalC2×C13×D35C13
cosocleC5×C7×C13C22×C13
LCSG ▷ C5×C7
UCSC1 ◁ C2×C169

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11830

Conjugacy classes & character table

6422 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23660, 34);