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C37×#557 #14557222

order2368
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C37 · Schur multiplier (H2) = C24

Aliases

direct productC37×#557

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C24
commutator, Frattini, cosocleC22C24×C37
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(46,47,49,51)(48,52,53,50);(38,39,41,42)(40,44,45,43);(46,48,49,53)(47,50,51,52);(38,40,41,45)(39,43,42,44)

Conjugacy classes & character table

925 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1626, C37×#1636, C37×#1648, …
maximal normal subgroup ofC37×#1626, C37×#1636, C37×#1648, …
maximal quotient ofQ8×C4⋊C4×C37, C37×#2351, C37×#2355, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 238);