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C5×#10069 #11932789

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

Aliases

direct productC5×#10069

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

566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5)(11,15)(12,13)(16,17)(18,19,23,27)(20,28,31,32)(21,24,22,26)(25,29,33,30);(6,7)(8,9)(10,11,14,16)(12,15,13,17)(19,24)(21,22)(25,32)(26,27)(28,33)(29,30);(7,9)(10,12,14,13)(11,15,16,17)(18,20,23,31)(19,25,27,33)(21,30,22,29)(24,32,26,28)

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, 3057);