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C5×#13452 #11936172

order1280
nilpotency class4
isoclinismisoclinic class of #13304
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#13452

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5C2×D8
commutator, Frattini, cosocleC22×C8C23×C5
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G

382 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)(10,11,14,16)(12,17,13,15)(18,19,21,26)(20,28,23,24)(22,25,30,33)(27,29,32,31);(6,7)(8,9)(10,12,14,13)(11,15,16,17)(18,20,21,23)(19,24,26,28)(22,29,30,31)(25,27,33,32);(7,9)(10,13,14,12)(11,15,16,17)(19,25)(20,23)(22,31)(24,32)(26,33)(27,28)(29,30)

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 6440);