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C37×#472 #14557137

order2368
nilpotency class3
isoclinismisoclinic class of #471
automorphism?
homologyAbelianization (H1) = C23×C37 · Schur multiplier (H2) = C22

Aliases

direct productC37×#472

Subgroups

subgroupG/H
center, socleC2×C37#121
commutator, Frattini, cosocleC2×C4C23×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C2×C4×C37 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#2192, C37×#2193, C37×#2221, …
maximal normal subgroup ofC37×#2192, C37×#2193, C37×#2221, …
maximal quotient ofC37×#1667, C37×#1668, C37×#1675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 153);