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C5×#10357 #11933077

order1280
nilpotency class3
isoclinismisoclinic class of #10046
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#10357

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

452 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)(6,7,9,11)(8,12,13,10)(15,18)(16,20)(19,21)(22,23,24,27)(25,26,29,28);(6,8,9,13)(7,10,11,12)(22,23)(24,27)(25,26)(28,29);(14,15,17,19)(16,21,20,18)(23,26)(25,29)(27,28)

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, 3345);