Finite Group Databasebeta

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C5×#19190 #11941910

order1280
nilpotency class3
isoclinismisoclinic class of #19186
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#19190

Subgroups

subgroupG/H
center, socleC22×C5C2×#121
commutator, Frattini, cosocleC42C24×C5
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 640

A minimal faithful permutation representation — 4 generators on 29 points:

(1,2,3,4,5)(6,7)(8,10)(9,12)(11,13)(14,15)(16,23)(17,21)(18,27)(19,22)(20,25)(24,28)(26,29);(14,16,17,24,19,26,18,25)(15,20,27,29,22,28,21,23);(7,10)(8,13)(11,12)(14,15)(16,20)(17,27)(18,21)(19,22)(23,25)(24,29)(26,28);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,23,28,29)

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 12178);