Finite Group Databasebeta

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C37×#560 #14557225

order2368
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C37 · Schur multiplier (H2) = C24

Aliases

direct productC37×#560

Subgroups

subgroupG/H
center, socleC22×C37C24
commutator, Frattini, cosocleC22C24×C37
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ G

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 592

A minimal faithful permutation representation — 4 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)(40,47)(41,46)(42,44)(43,49)(45,51)(48,52)(50,53);(38,40)(39,43)(41,49)(42,50)(44,52)(45,53)(46,47)(48,51);(39,44)(40,48)(43,47)(45,46)(49,50)(52,53);(39,45)(40,49)(43,52)(44,46)(47,53)(48,50)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#2200, C2×C37×#560, C37×#3529, …
maximal normal subgroup ofC37×#2200, C2×C37×#560, C37×#3529, …
maximal quotient ofC37×#2375, C37×#2376, C37×#2377, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 241);