Finite Group Databasebeta

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C4×C17×C169⋊C3 #46828124

order34476
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C169⋊C3
unambiguous semidirect product(C4×C169)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C169)⋊C3

Splittings

Fitting, HallC4×C17×C169 ⋊ C3
derived, SylowC169 ⋊ C3×C4×C17
HallC17×C169 ⋊ C3×C4
HallC4×C169 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C169⋊C3
commutator, hypocenterC169C3×C4×C17
FrattiniC2×C13C2×C17×C13⋊C3
FittingC4×C17×C169C3
socleC2×C13×C17C2×C13⋊C3
prime radicalC2×C17×C169⋊C3C2
cosocleC2×C169C2×C3×C17
LCSG ▷ C169
UCSC1 ◁ C4×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11492

Conjugacy classes & character table

4012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 5);