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Cayley diagram

C3×C43 #5248

order192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 172032
homologyAbelianization (H1) = G · Schur multiplier (H2) = C43

Aliases

abelianC3×C43

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C23×C3
socle, prime radicalC23×C3C23
LCSG ▷ C1
UCSC1 ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 15
transitive degreeμt(G) = 192

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

center ofC3×C4×#322, C3×#8131, C3×C42×M16, …
Fitting subgroup of#67611, C4×#805, C42×C3⋊C8, …
maximal subgroup of#67611, C3×#1276, C4×#805, …
maximal normal subgroup of#67611, C3×#1276, C4×#805, …
maximal quotient ofC3×C4×#95, C3×C42×C8, C3×C4×#97, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 807);