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C37×#442 #14557107

order2368
nilpotency class3
isoclinismisoclinic class of AGL(1,ℤ/8)
automorphism?
homologyAbelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C23

Aliases

direct productC37×#442

Subgroups

subgroupG/H
center, socleC22×C37C2×D4
commutatorC4C22×C4×C37
Frattini, cosocleC2×C4C23×C37
prime radicalC2×D8×C37C2
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 1184

A minimal faithful permutation representation — 3 generators on 49 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)(38,39,41,40)(42,43,45,47)(44,46,49,48);(43,46)(44,49)(47,48);(38,40,41,39)(43,47)(46,48)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×AGL(1,ℤ/16), C2×C37×#442, C37×#2943, …
maximal normal subgroup ofC37×AGL(1,ℤ/16), C2×C37×#442, C37×#2943, …
maximal quotient ofC37×#1580, C37×#1586, C37×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 123);