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C2×C5×#2514 #11957499

order1280
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×#2514

Subgroups

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

1942 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);(4,6)(5,9)(11,12,16,14)(13,18,17,15)(21,25)(23,26);(3,4,7,6)(5,8,9,10)(11,13)(12,15)(14,18)(16,17)(19,20,22,24)(21,26,25,23);(3,5)(4,8)(6,10)(7,9)(11,14,16,12)(13,18,17,15)(19,21,22,25)(20,23,24,26);(3,6,7,4)(5,10,9,8)(11,15,16,18)(12,17,14,13)

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 27767);