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C2×C19⋊C3×C169 #34064179

order19266
automorphism?
homologyAbelianization (H1) = C2×C3×C169 · Schur multiplier (H2) = C1

Aliases

direct productC2×C19⋊C3×C169
unambiguous semidirect product(C2×C19)⋊(C3×C169)

Splittings

Fitting, HallC2×C19×C169 ⋊ C3
derived, SylowC19 ⋊ C2×C3×C169
HallC19×C169 ⋊ C2×C3
HallC2×C19 ⋊ C3×C169

Subgroups

subgroupG/H
center, hypercenterC2×C169C19⋊C3
commutator, hypocenterC19C2×C3×C169
FrattiniC13C2×C13×C19⋊C3
FittingC2×C19×C169C3
socleC2×C13×C19C3×C13
prime radicalC2×C13×C19⋊C3C13
cosocleC13×C19C2×C3×C13
LCSG ▷ C19
UCSC1 ◁ C2×C169

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6422

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC169×(C19⋊C3)⋊C4, C19⋊C3×Dic169, (C19⋊C3)⋊Dic169, …
maximal normal subgroup ofC169×(C19⋊C3)⋊C4, C19⋊C3×Dic169, (C19⋊C3)⋊Dic169, …
maximal quotient ofC4×C19⋊C3×C169, C22×C19⋊C3×C169

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19266, 14);