Finite Group Databasebeta

← Prev (#11946129) Next (#11946131) →

C2×C5×#2008 #11946130

order1280
nilpotency class3
isoclinismisoclinic class of #2008
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×#2008

Subgroups

subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

2118 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)(5,13)(6,11)(7,10)(8,12)(9,14)(15,18)(16,17);(3,5)(4,9)(6,16)(7,14)(8,15)(10,18)(11,13)(12,17);(4,10)(6,7)(9,13)(11,12)(14,16)(17,18)

Conjugacy classes & character table

230 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, 16398);