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C5×#35346 #11958066

order1280
nilpotency class2
isoclinismisoclinic class of #35346
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C211

Aliases

direct productC5×#35346

Subgroups

subgroupG/H
center, socleC23×C5C25
commutator, Frattini, cosocleC23C25×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C5 ◁ G

7198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC5×#35346⋊C3, D5×#35346, D5×#35346⋊C3, …
maximal subgroup ofC5×#35346⋊C3, D5×#35346
maximal normal subgroup ofC5×#35346⋊C3, D5×#35346
maximal quotient ofC5×#6499874

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 28334);