Finite Group Databasebeta

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C3×Dic7×C169 #28382091

order14196
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C169 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic7×C169

Splittings

derived, SylowC7 ⋊ C3×C4×C169
HallC3×C7×C169 ⋊ C4
HallC7×C169 ⋊ C3×C4
HallC3×C7 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC2×C3×C169D7
commutator, hypocenterC7C3×C4×C169
FrattiniC2×C13C3×C13×D7
FittingC2×C3×C7×C169C2
socle, prime radicalC2×C3×C7×C13C2×C13
cosocleC2×C7×C13C2×C3×C13
LCSG ▷ C7
UCSC1 ◁ C2×C3×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14196, 19);