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C19×#2617 #14560474

order2432
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C24×C19 · Schur multiplier (H2) = C24×C4

Aliases

direct productC19×#2617

Subgroups

subgroupG/H
center, socleC23×C19C24
commutator, Frattini, cosocleC23C24×C19
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C19 ◁ G

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 608

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)(24,25,26,27)(28,29)(30,33)(31,32)(34,35);(21,23)(29,32)(33,34);(20,21)(22,23)(24,25)(26,27)(28,29)(30,34)(31,32)(33,35);(28,30)(29,33)(31,35)(32,34)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#9203, C19×#9205, C19×#9914, …
maximal normal subgroup ofC19×#9203, C19×#9205, C19×#9914, …
maximal quotient ofC19×#14255, C19×#14259, C19×#14271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1349);