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#16864282⋊C3 #27166148

order12876
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#16864282⋊C3

Splittings

Fitting, socle, derived, HallC29×C37 ⋊ C3×C4
Hall#16864282 ⋊ C3
HallC29×C37⋊C3 ⋊ C4
HallC37⋊C3 ⋊ #1181
SylowC37 ⋊ C3×#1181
SylowC29 ⋊ Dic37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC29×C37C3×C4
prime radicalD29×C37⋊C3C2
cosocleC37×D29C2×C3
LCSG ▷ C29×C37
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 1073

A minimal faithful permutation representation — 2 generators on 66 points:

(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(39,40,41,43)(42,45,46,52)(44,49,50,48)(47,54,55,63)(51,56,58,60)(53,61,62,57)(59,64,65,66);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)(38,39,42,47,56,45,53,63,66,65,58,50,43,48,57,61,49,40,44,51,59,64,54,62,52,60,55,46,41)

Polycyclic presentation:

2,3,2,29,37|a^2=c,d^a=d^17,e^a=e^36,e^b=e^26,d^c=d^28

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#50311194, C3×#16864282⋊C3, C3⋊(#16864282⋊C3)
maximal normal subgroup of#50311194, C3×#16864282⋊C3
maximal quotient of#50311130, C3×#16864282⋊C3, C3⋊(#16864282⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 17);