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C2×C5×#3019 #11983103

order1280
nilpotency class3
isoclinismisoclinic class of #3019
automorphism?
homologyAbelianization (H1) = C25×C5 · Schur multiplier (H2) = C210

Aliases

direct productC2×C5×#3019

Subgroups

subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC2×C4C25×C5
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

5118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 5 generators on 23 points:

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

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, 53371);