Finite Group Databasebeta

← Prev (#37529044) Next (#37529046) →

C29⋊((C19⋊C3)⋊D7) #37529045

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

Aliases

unambiguous semidirect productC29⋊((C19⋊C3)⋊D7)
unambiguous semidirect product(C19⋊C3)⋊D203

Splittings

Fitting, socle, derived, HallC7×C19×C29 ⋊ C2×C3
HallC7×C29×C19⋊C3 ⋊ C2
HallD3857 ⋊ C3
HallC29×C19⋊C3 ⋊ D7
HallC19×C29 ⋊ C3×D7
HallC7×C19⋊C3 ⋊ D29
HallC7×C29 ⋊ D19⋊C3
HallC7×C19 ⋊ C3×D29
HallC19⋊C3 ⋊ D203
SylowC29 ⋊ (C19⋊C3)⋊D7
SylowC19 ⋊ C3×D203
SylowC7 ⋊ C29⋊(D19⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C19×C29C2×C3
LCSG ▷ C7×C19×C29
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 3857

A minimal faithful permutation representation — 2 generators on 55 points:

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

Polycyclic presentation:

2,3,7,19,29|c^a=c^6,d^a=d^18,e^a=e^28,d^b=d^7

Conjugacy classes & character table

918 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23142, 54);