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C5×#16464 #11939184

order1280
nilpotency class2
isoclinismisoclinic class of #16249
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#16464

Subgroups

subgroupG/H
center, socle, prime radicalC24×C5C24
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 29 points:

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

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, 9452);