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C37×#500 #14557165

order2368
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C23×C37 · Schur multiplier (H2) = C22

Aliases

direct productC37×#500

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C2×D4
commutator, Frattini, cosocleC2×C4C23×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 2368

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,41,43)(40,44,45,42)(47,50)(48,51)(52,53);(38,40,41,45)(39,42,43,44);(46,47,51,53,49,52,48,50)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1364, C37×#1365, C37×#1647, …
maximal normal subgroup ofC37×#1364, C37×#1365, C37×#1647, …
maximal quotient ofC37×#1845, C37×#1942, C37×#1990, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 181);