Finite Group Databasebeta

← Prev (#27166148) Next (#27166150) →

C37⋊C3×#1181 #27166149

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

Aliases

direct productC37⋊C3×#1181
unambiguous semidirect product(C37×#1181)⋊C3

Splittings

Fitting, socle, derived, HallC29×C37 ⋊ C3×C4
HallC37×#1181 ⋊ C3
HallC29×C37⋊C3 ⋊ C4
SylowC37 ⋊ C3×#1181
SylowC29 ⋊ C4×C37⋊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:

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

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#1181×#66526, C3×C37⋊C3×#1181, C37⋊C3×C3⋊#1181
maximal normal subgroup of#1181×#66526, C3×C37⋊C3×#1181
maximal quotient of#1181×#66524, C3×C37⋊C3×#1181, C37⋊C3×C3⋊#1181

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 18);