Finite Group Databasebeta

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C2×D21×C169 #28382147

order14196
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C169 · Schur multiplier (H2) = C2

Aliases

direct productC2×D21×C169
unambiguous semidirect product(C2×C3)⋊(D7×C169)
unambiguous semidirect product(C2×C7)⋊(D3×C169)

Splittings

FittingC2×C3×C7×C169 ⋊ C2
derived, HallC3×C7 ⋊ C22×C169
HallC3×C7×C169 ⋊ C22
HallC7×C169 ⋊ C2×D3
HallC3×C169 ⋊ C2×D7
SylowC7 ⋊ C2×D3×C169
SylowC3 ⋊ C2×D7×C169

Subgroups

subgroupG/H
center, hypercenterC2×C169D21
commutator, hypocenterC3×C7C22×C169
FrattiniC13C2×C13×D21
FittingC2×C3×C7×C169C2
socleC2×C3×C7×C13C2×C13
prime radicalC2×C13×D21C13
cosocleC3×C7×C13C22×C13
LCSG ▷ C3×C7
UCSC1 ◁ C2×C169

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14196, 75);