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C19×#1416 #14559273

order2432
nilpotency class5
isoclinismisoclinic class of D32
automorphism?
homologyAbelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×#1416

Subgroups

subgroupG/H
center, socle, prime radicalC22×C19D16
commutatorC16C2×C4×C19
Frattini, cosocleC2×C16C22×C19
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C4×C19 ◁ C2×C8×C19 ◁ C2×C16×C19 ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 2432

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(25,30)(26,34)(27,36)(28,40)(31,46)(32,49)(33,45)(35,39)(37,53)(38,43)(41,47)(42,44)(48,54)(50,51)(52,55);(24,25,29,33)(26,35,38,52)(27,39,41,55)(28,42,40,32)(30,43,45,34)(31,47,48,36)(37,54,50,46)(44,51,49,53)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×#1416, C19×#13615, C19×#13616, …
maximal normal subgroup ofC2×C19×#1416, C19×#13615, C19×#13616, …
maximal quotient ofC19×#7384, C19×#7419, C19×#7445, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 148);