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C3×D4147 #38733456

order24882
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4147
unambiguous semidirect productC11⋊(C3×D377)
unambiguous semidirect productC29⋊(C3×D143)

Splittings

Fitting, socle, HallC3×C11×C13×C29 ⋊ C2
derived, HallC11×C13×C29 ⋊ C2×C3
HallC3×C13×C29 ⋊ D11
HallC3×C11×C29 ⋊ D13
HallC3×C11×C13 ⋊ D29
HallC13×C29 ⋊ C3×D11
HallC11×C29 ⋊ C3×D13
HallC11×C13 ⋊ C3×D29
HallC3×C29 ⋊ D143
HallC3×C13 ⋊ D319
HallC3×C11 ⋊ D377
SylowC29 ⋊ C3×D143
SylowC13 ⋊ C3×D319
SylowC11 ⋊ C3×D377

Subgroups

subgroupG/H
center, hypercenterC3D4147
commutator, cosocle, hypocenterC11×C13×C29C2×C3
FrattiniC1G
Fitting, socleC3×C11×C13×C29C2
LCSG ▷ C11×C13×C29
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 12441

A minimal faithful permutation representation — 2 generators on 56 points:

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

Conjugacy classes & character table

6225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24882, 9);