Finite Group Databasebeta

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Cayley diagram

C3×#3866 #89225

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

Aliases

direct productC3×#3866

Splittings

Fitting, socle, HallC3×C37 ⋊ C4
derived, SylowC37 ⋊ C3×C4

Subgroups

subgroupG/H
center, hypercenterC3#3866
commutator, hypocenterC37C3×C4
FrattiniC1G
Fitting, socleC3×C37C4
prime radicalC3×D37C2
cosocleD37C2×C3
LCSG ▷ C37
UCSC1 ◁ C3

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:

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

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#3866, C2×C3×#3866, #13050613, …
maximal normal subgroup ofD3×#3866, C2×C3×#3866, #13050613, …
maximal quotient ofC3×#64438, C2×C3×#3866, C9×#3866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 9);