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C37×#1412 #17990230

order4736
nilpotency class5
isoclinismisoclinic class of #1412
automorphism?
homologyAbelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C4

Aliases

direct productC37×#1412

Subgroups

subgroupG/H
center, socleC2×C37#354
commutatorC42C2×C4×C37
Frattini, cosocle#127C22×C37
prime radical#127×C37C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C22×C37 ◁ C2×C4×C37 ◁ #127×C37 ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

518 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#7523, C37×#7524, C2×C37×#1412, …
maximal normal subgroup ofC37×#7523, C37×#7524, C2×C37×#1412, …
maximal quotient ofC37×#7358, C37×#7367, C37×#7412, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 144);