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C37×#347 #14557012

order2368
nilpotency class2
isoclinismisoclinic class of H(3,ℤ/4)
automorphism?
homologyAbelianization (H1) = C42×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×#347

Subgroups

subgroupG/H
centerC4×C37C42
commutatorC4C42×C37
Frattini, cosocleC2×C8C22×C37
socleC2×C37#97
prime radicalC22×C37M16
LCSG ▷ C4 ▷ C1
UCSC1 ◁ C4×C37 ◁ G

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(38,39,40,44,41,46,48,52,42,45,47,53,49,43,50,51);(39,43,45,46)(40,47)(44,52,53,51)(48,50)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1355, C37×#1356, C2×C37×#347, …
maximal normal subgroup ofC37×#1355, C37×#1356, C2×C37×#347, …
maximal quotient ofC37×#1313, C37×#1375, C2×C37×#347

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 28);