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C5×#24171 #11946891

order1280
nilpotency class3
isoclinismisoclinic class of #23876
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#24171

Subgroups

subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

1106 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)(9,10)(11,13)(14,15,19,23)(16,20,26,29)(17,21,18,22)(24,27,25,28);(7,10)(11,12)(14,16)(15,20)(17,25)(18,24)(19,26)(21,28)(22,27)(23,29);(15,21)(16,24)(17,18)(22,23)(25,26)(27,28);(6,8,9,13)(7,11,10,12)

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, 17159);