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#16864280⋊C3 #27166146

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

Aliases

unambiguous semidirect product#16864280⋊C3

Splittings

Fitting, socle, derived, HallC29×C37 ⋊ C3×C4
Hall#16864280 ⋊ C3
HallC29×C37⋊C3 ⋊ C4
HallC37⋊C3 ⋊ #1181
SylowC37 ⋊ C3×#1181
SylowC29 ⋊ #3866⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC29×C37C3×C4
prime radicalC29⋊(D37⋊C3)C2
cosocleD1073C2×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:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#50311192, C3×#16864280⋊C3, C3⋊(#16864280⋊C3)
maximal normal subgroup of#50311192, C3×#16864280⋊C3
maximal quotient of#50311128, C3×#16864280⋊C3, C3⋊(#16864280⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 15);