Finite Group Databasebeta

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C2×C5×#1906 #11943719

order1280
nilpotency class3
isoclinismisoclinic class of #471
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×#1906

Subgroups

subgroupG/H
centerC2×C4×C5#121
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
socleC22×C5#386
prime radicalC2×C5×#575C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ G

1798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 160

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2)(19,20,21,22,23);(3,4)(5,8,12,18)(6,11)(7,10)(9,13,17,14)(15,16);(3,5)(4,8,10,18)(6,14)(7,12)(9,16,17,11)(13,15);(3,5)(4,9)(6,14)(7,12)(8,16)(10,17)(11,18)(13,15)

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×#23872
maximal normal subgroup ofC2×C5×#23872

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 13987);