Finite Group Databasebeta

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C3×AGL(1,𝔽5)×C169⋊C3 #44477489

order30420
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽5)×C169⋊C3
unambiguous semidirect product(AGL(1,𝔽5)×C169)⋊C32
unambiguous semidirect product(C3×AGL(1,𝔽5)×C169)⋊C3

Splittings

FittingC3×C5×C169 ⋊ C3×C4
derived, HallC5×C169 ⋊ C32×C4
HallC3×C5×C169⋊C3 ⋊ C4
HallAGL(1,𝔽5)×C169 ⋊ C32
SylowC169 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×C169⋊C3

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽5)×C169⋊C3
commutator, hypocenterC5×C169C32×C4
FrattiniC13C3×AGL(1,𝔽5)×C13⋊C3
FittingC3×C5×C169C3×C4
socleC3×C5×C13C4×C13⋊C3
prime radicalC3×D5×C169⋊C3C2
cosocleD5×C169C2×C32
LCSG ▷ C5×C169
UCSC1 ◁ C3

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2535

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 78);