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Cayley diagram

C3⋊#3866 #89226

order444
isoclinismisoclinic class of C3⋊#3866
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#3866

Splittings

Fitting, socle, derived, HallC3×C37 ⋊ C4
SylowC37 ⋊ Dic3
SylowC3 ⋊ #3866

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C37C4
prime radical, cosocleC3×D37C2
LCSG ▷ C3×C37
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 111

A minimal faithful permutation representation — 2 generators on 40 points:

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

Polycyclic presentation:

2^2,3,37|a^2=b,c^a=c^2,d^a=d^6,d^b=d^36

Conjugacy classes & character table

33 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3866, C2×C3⋊#3866, C9⋊#3866, …
maximal normal subgroup ofD3×#3866, C2×C3⋊#3866, C3⋊(#3866⋊C3), …
maximal quotient ofC3⋊#64438, C2×C3⋊#3866, C9⋊#3866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 10);