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C5×#18640 #11941360

order1280
nilpotency class3
isoclinismisoclinic class of #18618
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#18640

Subgroups

subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

1210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 320

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

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

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, 11628);