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C19×#24464 #18030423

order4864
nilpotency class3
isoclinismisoclinic class of #24464
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C26

Aliases

direct productC19×#24464

Subgroups

subgroupG/H
center, socleC22×C19C2×#120
commutator, Frattini, cosocleC22×C4C24×C19
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G

1600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 608

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 17452);