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C5×AGL(1,𝔽17) #13062852

order1360
isoclinismisoclinic class of AGL(1,𝔽17)
automorphism?
homologyAbelianization (H1) = C5×C16 · Schur multiplier (H2) = C1

Aliases

direct productC5×AGL(1,𝔽17)

Splittings

Fitting, socle, HallC5×C17 ⋊ C16
derived, SylowC17 ⋊ C5×C16

Subgroups

subgroupG/H
center, hypercenterC5AGL(1,𝔽17)
commutator, hypocenterC17C5×C16
FrattiniC1G
Fitting, socleC5×C17C16
prime radicalC5×D17C8
cosocle#3633C2×C5
LCSG ▷ C17
UCSC1 ◁ C5

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 85

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4,5)(7,8,9,13,10,14,17,20,11,15,18,21,16,22,12,19);(6,7,12,8,16,14,19,21,18,9,13,20,22,10,15,17,11)

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AGL(1,𝔽17), C52×AGL(1,𝔽17), C2×C5×AGL(1,𝔽17), …
maximal normal subgroup ofD5×AGL(1,𝔽17), C52×AGL(1,𝔽17), C2×C5×AGL(1,𝔽17), …
maximal quotient ofC52×AGL(1,𝔽17), C2×C5×AGL(1,𝔽17), C5×#13062855, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 220);