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#16864281⋊C3 #27166147

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

Aliases

unambiguous semidirect product#16864281⋊C3

Splittings

Fitting, socle, derived, HallC29×C37 ⋊ C3×C4
Hall#16864281 ⋊ 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:

(2,7,12,8,4,17,5,18,10,3,11,24)(6,26,34,27,14,19,15,37,29,13,30,25)(9,36,32,20,22,28,23,31,35,21,16,33)(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);(1,2,6,16,32,21,3,9,7,19,10,11,13,28,24,14,26,34,31,36,29,37,30,17,33,27,4,12,25,18,23,8,20,35,22,15,5)(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^6,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#50311193, C3×#16864281⋊C3, C3⋊(#16864281⋊C3)
maximal normal subgroup of#50311193, C3×#16864281⋊C3
maximal quotient of#50311129, C3×#16864281⋊C3, C3⋊(#16864281⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 16);