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C2×C5×#1914 #11943735

order1280
nilpotency class3
isoclinismisoclinic class of #1913
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×#1914

Subgroups

subgroupG/H
center, socleC22×C5#386
commutatorC23C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#535C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

1862 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);(3,4,7,11,8,10,17,5)(6,13,15,18,14,9,16,12);(3,5,7,10,8,11,17,4)(6,12,16,13,14,18,15,9);(3,6)(4,9)(5,12)(7,16)(8,14)(10,13)(11,18)(15,17)

Conjugacy classes & character table

290 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, 14003);