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C2×C3×C5×#487 #14276163

order1920
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×C3×C5×#487

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3×C5C2×D4
commutator, Frattini, cosocleC2×C4C24×C3×C5
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ C2×C3×C42×C5 ◁ G

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 1861);