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C19×#13910 #18019869

order4864
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4

Aliases

direct productC19×#13910

Subgroups

subgroupG/H
center, socle, prime radicalC24×C19C24
commutatorC23C23×C4×C19
Frattini, cosocleC24C24×C19
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 4864

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6898);