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C9×C7⋊AGL(1,𝔽5) #11929468

order1260
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊AGL(1,𝔽5)

Splittings

Fitting, HallC5×C7×C9 ⋊ C4
derived, HallC5×C7 ⋊ C4×C9
HallC7×C9 ⋊ AGL(1,𝔽5)
HallC5×C9 ⋊ Dic7
SylowC7 ⋊ C9×AGL(1,𝔽5)
SylowC5 ⋊ C9×Dic7

Subgroups

subgroupG/H
center, hypercenterC9C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C9
FrattiniC3C3×C7⋊AGL(1,𝔽5)
FittingC5×C7×C9C4
socleC3×C5×C7C3×C4
prime radical, cosocleC3×C7×D5C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 315

A minimal faithful permutation representation — 2 generators on 21 points:

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

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C11×C7⋊AGL(1,𝔽5), C9×C7⋊(C11⋊AGL(1,𝔽5)), #30655040, …
maximal normal subgroup ofC9×C11×C7⋊AGL(1,𝔽5), C9×C13×C7⋊AGL(1,𝔽5), C9×C17×C7⋊AGL(1,𝔽5), …
maximal quotient ofC9×C11×C7⋊AGL(1,𝔽5), C9×C7⋊(C11⋊AGL(1,𝔽5)), #30655040, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 20);