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C37×#332 #14556997

order2368
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C2

Aliases

direct productC37×#332

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C22⋊C4
commutatorC2×C4C2×C4×C37
Frattini, cosocleC42C22×C37
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 2368

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C37×#332, C37×#1540, C37×#1542, …
maximal normal subgroup ofC2×C37×#332, C37×#1540, C37×#1542, …
maximal quotient ofC37×#1271, C37×#1296, C37×#1363, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 13);