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C3×AGL(1,𝔽17) #11717915

order816
isoclinismisoclinic class of AGL(1,𝔽17)
automorphism?
homologyAbelianization (H1) = C3×C16 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽17)

Splittings

Fitting, socle, HallC3×C17 ⋊ C16
derived, SylowC17 ⋊ C3×C16

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽17)
commutator, hypocenterC17C3×C16
FrattiniC1G
Fitting, socleC3×C17C16
prime radicalC3×D17C8
cosocle#3633C2×C3
LCSG ▷ C17
UCSC1 ◁ C3

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 51

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3)(5,6,7,11,8,12,15,18,9,13,16,19,14,20,10,17);(4,5,10,6,14,12,17,19,16,7,11,18,20,8,13,15,9)

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽17), C2×C3×AGL(1,𝔽17), A4×AGL(1,𝔽17), …
maximal normal subgroup ofD3×AGL(1,𝔽17), C2×C3×AGL(1,𝔽17), C32×AGL(1,𝔽17), …
maximal quotient ofC3×#10587664, C2×C3×AGL(1,𝔽17), A4×AGL(1,𝔽17), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(816, 185);