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C37×#357 #14557022

order2368
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C22

Aliases

direct productC37×#357

Subgroups

subgroupG/H
center, socleC22×C37D8
commutatorC8C2×C4×C37
Frattini, cosocleC2×C8C22×C37
prime radicalC2×D8×C37C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C4×C37 ◁ C2×C8×C37 ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1184

A minimal faithful permutation representation — 2 generators on 57 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)(38,39,40,41)(42,43)(44,47)(45,54)(46,50)(48,51)(49,52)(53,56)(55,57);(43,47)(44,51)(45,52)(48,49)(50,56)(53,57)(54,55)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C37×#357, C37×#2138, C37×#2139, …
maximal normal subgroup ofC2×C37×#357, C37×#2138, C37×#2139, …
maximal quotient ofC37×#1331, C37×#1347, C37×#1361, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 38);