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C5×#29831 #11952551

order1280
nilpotency class3
isoclinismisoclinic class of #29592
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#29831

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 33 points:

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

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, 22819);