Finite Group Databasebeta

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C37×#534 #14557199

order2368
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C37 · Schur multiplier (H2) = C25

Aliases

direct productC37×#534

Subgroups

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

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 592

A minimal faithful permutation representation — 4 generators on 49 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)(39,41)(42,43)(44,48)(45,46)(47,49);(43,46)(47,48);(38,39)(40,41)(42,43)(44,47)(45,46)(48,49);(42,44)(43,47)(45,49)(46,48)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1595, C37×#1601, C37×#1607, …
maximal normal subgroup ofC37×#1595, C37×#1601, C37×#1607, …
maximal quotient ofC37×#2308, C37×#2315, C37×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 215);