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C2×C3×C5×#454 #14276050

order1920
nilpotency class3
isoclinismisoclinic class of #453
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26

Aliases

direct productC2×C3×C5×#454

Subgroups

subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC2×C4C24×C3×C5
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

1456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1748);