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C37×#562 #14557227

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

Aliases

direct productC37×#562

Subgroups

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

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1184

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)(39,42)(40,44)(46,47)(48,52)(49,50)(51,53);(39,42)(43,45)(47,50)(51,52);(38,39)(40,43)(41,42)(44,45)(46,48,49,53)(47,51,50,52);(38,40)(39,43)(41,44)(42,45)(46,47)(48,51)(49,50)(52,53)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1656, C37×#1661, C37×#1662, …
maximal normal subgroup ofC37×#1656, C37×#1661, C37×#1662, …
maximal quotient ofC37×#2376, C37×#2377, C37×#2378, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 243);