Finite Group Databasebeta

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C5×#23882 #11946602

order1280
nilpotency class3
isoclinismisoclinic class of #23882
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C27

Aliases

direct productC5×#23882

Subgroups

subgroupG/H
center, socleC2×C5#2403
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ G

1866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 80

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#23882
maximal normal subgroup ofD5×#23882

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 16870);