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C37×#487 #14557152

order2368
nilpotency class3
isoclinismisoclinic class of #465
automorphism?
homologyAbelianization (H1) = C23×C37 · Schur multiplier (H2) = C4

Aliases

direct productC37×#487

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

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1635, C37×#1636, C37×#1637, …
maximal normal subgroup ofC37×#1635, C37×#1636, C37×#1637, …
maximal quotient ofC37×#1834, C37×#1933, C37×#1956, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 168);