Finite Group Databasebeta

← Prev (#11941906) Next (#11941908) →

C5×#19187 #11941907

order1280
nilpotency class3
isoclinismisoclinic class of #19186
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct productC5×#19187

Subgroups

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

842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 320

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

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

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, 12175);