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C37×#330 #14556995

order2368
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×#330

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C22⋊C4
commutatorC2×C4C2×C4×C37
Frattini, cosocleC42C22×C37
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 2368

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C37×#330, C37×#1524, C37×#1526, …
maximal normal subgroup ofC2×C37×#330, C37×#1524, C37×#1526, …
maximal quotient ofC37×#1271, C37×#1295, C2×C37×#330

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 11);