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C2×C5×#2839 #11959381

order1280
nilpotency class2
isoclinismisoclinic class of #2812
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×#2839

Subgroups

subgroupG/H
center, socle, prime radicalC24×C5C24
commutator, Frattini, cosocleC23C25×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C5 ◁ G

1654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 1280

A minimal faithful permutation representation — 5 generators on 31 points:

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

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, 29649);