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C37×#496 #14557161

order2368
nilpotency class3
isoclinismisoclinic class of #468
automorphism?
homologyAbelianization (H1) = C23×C37 · Schur multiplier (H2) = C2×C4

Aliases

direct productC37×#496

Subgroups

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

144 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)(39,41)(43,46)(44,48)(47,49);(42,43,44,46,45,47,48,49);(38,39,40,41)(43,47)(46,49)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1406, C37×#1655, C37×#1656, …
maximal normal subgroup ofC37×#1406, C37×#1655, C37×#1656, …
maximal quotient ofC37×#1714, C37×#1715, C37×#1717, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 177);