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(C19⋊C3)⋊#64418 #30660730

order16758
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C19⋊C3)⋊#64418

Splittings

Fitting, socle, HallC72×C19 ⋊ C3×D3
derivedC19×#3862 ⋊ C2×C3
HallC19⋊C3×#3862 ⋊ C2
SylowC72 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ C3×#64418

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC19×#3862C2×C3
Fitting, socleC72×C19C3×D3
LCSG ▷ C19×#3862
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 266

A minimal faithful permutation representation — 2 generators on 33 points:

(1,4,14,11,10,6,8,9,13,2,3,12,7,5)(16,20,21,17,18,22)(19,28,25,23,24,30)(26,31,33,32,29,27);(3,7,8)(4,9,6)(5,11,12)(10,14,13)(15,16,19,25,31,28,32,18,22,27,33,21,20,26,24,29,30,23,17)

Polycyclic presentation:

2,3^2,19,7^2|c^a=c^2,d^a=d^18,e^a=e^2f^3,f^a=e^6f^5,d^b=d^7,e^c=e^4f^4,f^c=f^2

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×#64418, #45691988, #45691989, …
maximal normal subgroup ofD19⋊C3×#64418, #45691988, #45691989, …
maximal quotient of(C19⋊C3)⋊#10596868, C2×(C19⋊C3)⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 257);