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C37×H(3,ℤ/4) #14557002

order2368
nilpotency class2
isoclinismisoclinic class of H(3,ℤ/4)
automorphism?
homologyAbelianization (H1) = C42×C37 · Schur multiplier (H2) = C2×C4

Aliases

direct productC37×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC4×C37C42
commutatorC4C42×C37
Frattini, cosocleC22×C4C22×C37
socleC2×C37#95
prime radicalC23×C37D4
LCSG ▷ C4 ▷ C1
UCSC1 ◁ C4×C37 ◁ G

94 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)(40,46,48,52)(41,44)(42,45)(43,47,50,53)(49,51);(38,40)(39,43,45,50)(41,47)(42,48)(44,46,51,52)(49,53)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1339, C37×#1340, C2×C37×H(3,ℤ/4), …
maximal normal subgroup ofC37×#1339, C37×#1340, C2×C37×H(3,ℤ/4), …
maximal quotient ofC37×#1274, C37×#1275, C37×#1284, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 18);