Finite Group Databasebeta

← Prev (#5264) Next (#5266) →

Cayley diagram

C3×#391 #5265

order192
nilpotency class2
isoclinismisoclinic class of #120
automorphismAut(G) order 4096
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#391

Subgroups

subgroupG/H
center, socle, prime radicalC23×C3C23
commutatorC22C22×C3×C4
Frattini, cosocleC23C23×C3
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 192

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2,4,3)(5,6,7,8)(9,10,12,14)(11,15,16,13)(17,18,19);(1,3,4,2)(6,8);(9,11,12,16)(10,13,14,15)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#67642, #67643, #67644, …
maximal subgroup of#67642, #67643, #67644, …
maximal normal subgroup of#67642, #67643, #67644, …
maximal quotient ofC3×C4⋊#95, C3×#1436, C3×#1441, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 824);