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C5×#19230 #11941950

order1280
nilpotency class3
isoclinismisoclinic class of #19230
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#19230

Subgroups

subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

790 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)(8,10)(9,12)(11,13)(15,19)(17,24)(20,25)(21,26)(23,28)(27,29);(14,15,17,19,18,21,24,26)(16,20,23,25,22,27,28,29);(7,10)(8,13)(11,12)(14,16)(15,20)(17,23)(18,22)(19,25)(21,27)(24,28)(26,29);(15,21)(16,22)(19,26)(23,28)

Conjugacy classes & character table

215 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 12218);