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C19×#13451 #18019410

order4864
nilpotency class4
isoclinismisoclinic class of #13304
automorphism?
homologyAbelianization (H1) = C23×C19 · Schur multiplier (H2) = C23

Aliases

direct productC19×#13451

Subgroups

subgroupG/H
center, socle, prime radicalC23×C19C2×D8
commutator, Frattini, cosocleC22×C8C23×C19
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 4864

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6439);