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C37×#2104 #17990922

order4736
nilpotency class3
isoclinismisoclinic class of #2104
automorphism?
homologyAbelianization (H1) = C23×C37 · Schur multiplier (H2) = C2

Aliases

direct productC37×#2104

Subgroups

subgroupG/H
center, socleC2×C37#401
commutator, Frattini, cosocleC24C23×C37
prime radicalC24×C37C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C24×C37 ◁ G

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 592

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

Conjugacy classes & character table

851 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C37×#2104, C37×#23847, C37×#32700, …
maximal normal subgroup ofC2×C37×#2104, C37×#23847, C37×#32700, …
maximal quotient ofC37×#10690, C37×#10691, C37×#11318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 836);