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C2×C19×#562 #14561384

order2432
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C25×C19 · Schur multiplier (H2) = C28

Aliases

direct productC2×C19×#562

Subgroups

subgroupG/H
center, socleC23×C19C24
commutator, Frattini, cosocleC22C25×C19
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

1152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1216

A minimal faithful permutation representation — 5 generators on 37 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(4,7)(5,9)(11,12)(13,17)(14,15)(16,18);(4,7)(8,10)(12,15)(16,17);(3,4)(5,8)(6,7)(9,10)(11,13,14,18)(12,16,15,17);(3,5)(4,8)(6,9)(7,10)(11,12)(13,16)(14,15)(17,18)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#8508, C2×C19×#1656, C2×C19×#1661, …
maximal normal subgroup ofC19×#8508, C2×C19×#1656, C2×C19×#1661, …
maximal quotient ofC2×C19×#2376, C2×C19×#2377, C2×C19×#2378, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2259);