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C37×#441 #14557106

order2368
nilpotency class3
isoclinismisoclinic class of AGL(1,ℤ/8)
automorphism?
homologyAbelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C22

Aliases

direct productC37×#441

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C2×D4
commutatorC4C22×C4×C37
Frattini, cosocleC2×C4C23×C37
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 2368

A minimal faithful permutation representation — 3 generators on 57 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)(38,39,41,40)(42,43)(44,50)(45,53)(46,48)(47,51)(49,55)(52,57)(54,56);(42,44,46,52)(43,47,48,56)(45,54,55,51)(49,57,53,50);(38,40,41,39)(43,48)(47,56)(49,53)(50,57)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#2180, C2×C37×#441, C37×#2943, …
maximal normal subgroup ofC37×#2180, C2×C37×#441, C37×#2943, …
maximal quotient ofC37×#1579, C37×#1587, C37×#1593, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 122);