Finite Group Databasebeta

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C37×#3194 #17992012

order4736
nilpotency class3
isoclinismisoclinic class of #3192
automorphism?
homologyAbelianization (H1) = C24×C37 · Schur multiplier (H2) = C24

Aliases

direct productC37×#3194

Subgroups

subgroupG/H
center, socleC22×C37C22×D4
commutator, Frattini, cosocleC2×C4C24×C37
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1184

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

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#9332, C37×#18322, C37×#18330, …
maximal normal subgroup ofC37×#9332, C37×#18322, C37×#18330, …
maximal quotient ofC37×#21767, C37×#21769, C37×#21944, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1926);