Finite Group Databasebeta

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C2×C5×#1648 #11941219

order1280
nilpotency class3
isoclinismisoclinic class of #1619
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#1648

Subgroups

subgroupG/H
center, socle, prime radicalC23×C5#120
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ G

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 31 points:

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

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, 11487);