Finite Group Databasebeta

← Prev (#37529004) Next (#37529006) →

C3×D3857 #37529005

order23142
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3857
unambiguous semidirect productC29⋊(C3×D133)

Splittings

Fitting, socle, HallC3×C7×C19×C29 ⋊ C2
derived, HallC7×C19×C29 ⋊ C2×C3
HallC3×C19×C29 ⋊ D7
HallC3×C7×C29 ⋊ D19
HallC19×C29 ⋊ C3×D7
HallC3×C7×C19 ⋊ D29
HallC7×C29 ⋊ C3×D19
HallC7×C19 ⋊ C3×D29
HallC3×C29 ⋊ D133
HallC3×C19 ⋊ D203
SylowC29 ⋊ C3×D133
HallC3×C7 ⋊ D551
SylowC19 ⋊ C3×D203
SylowC7 ⋊ C3×D551

Subgroups

subgroupG/H
center, hypercenterC3D3857
commutator, cosocle, hypocenterC7×C19×C29C2×C3
FrattiniC1G
Fitting, socleC3×C7×C19×C29C2
LCSG ▷ C7×C19×C29
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 58
transitive degreeμt(G) = 11571

A minimal faithful permutation representation — 2 generators on 58 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)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(5,10)(6,9)(7,8)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

5790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 14);