Finite Group Databasebeta

← Prev (#14560111) Next (#14560113) →

C19×#2255 #14560112

order2432
nilpotency class4
isoclinismisoclinic class of #2218
automorphism?
homologyAbelianization (H1) = C23×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×#2255

Subgroups

subgroupG/H
center, socle, prime radicalC22×C19C2×D8
commutator, Frattini, cosocleC2×C8C23×C19
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C42×C19 ◁ C4×C8×C19 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 2432

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC19×#12400, C19×#12401, C19×#12402, …
maximal normal subgroup ofC19×#12400, C19×#12401, C19×#12402, …
maximal quotient ofC19×#12908, C19×#13167, C19×#13168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 987);