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C5×#10575 #11933295

order1280
nilpotency class3
isoclinismisoclinic class of #10046
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#10575

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5#120
commutator, Frattini, cosocleC2×C42C23×C5
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 3 generators on 29 points:

(1,2,3,4,5)(6,7,10,12)(8,13,9,11)(14,15)(16,18)(17,20)(19,21)(22,23,25,28)(24,27,29,26);(6,8,10,9)(7,11,12,13)(22,24,25,29)(23,26,28,27);(6,9,10,8)(7,11,12,13)(15,18)(16,21)(19,20)(23,24)(26,27)(28,29)

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 3563);