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C3×AGL(1,𝔽5)×C289 #31773198

order17340
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C289 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C289

Splittings

Fitting, HallC3×C5×C289 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C289
HallC5×C289 ⋊ C3×C4
HallC3×C5 ⋊ C4×C289

Subgroups

subgroupG/H
center, hypercenterC3×C289AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C289
FrattiniC17C3×C17×AGL(1,𝔽5)
FittingC3×C5×C289C4
socleC3×C5×C17C4×C17
prime radicalC3×D5×C17C2×C17
cosocleD5×C17C2×C3×C17
LCSG ▷ C5
UCSC1 ◁ C3×C289

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4335

Conjugacy classes & character table

4335 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17340, 11);