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C5×#18524 #11941244

order1280
nilpotency class3
isoclinismisoclinic class of #18524
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#18524

Subgroups

subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

1716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal quotient ofC5×#489347

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 11512);