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C3⋊#19150312 #30660848

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

Aliases

unambiguous semidirect productC3⋊#19150312

Splittings

Fitting, socle, derivedC3×C72×C19 ⋊ C2×C3
HallC3×#14584116 ⋊ C2
HallC72×C19 ⋊ C3×D3
SylowC72 ⋊ C3⋊(D19⋊C3)
SylowC19 ⋊ D3×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C19C2×C3
LCSG ▷ C3×C72×C19
UCSC1

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 2793

A minimal faithful permutation representation — 3 generators on 36 points:

(2,6,7,3,4,8)(5,13,14,9,10,18)(11,19,17,16,15,12)(21,22)(24,25,26)(27,29,28)(31,32,33)(34,36,35);(1,2,5,10,15,18,17,7,6,11,16,4,8,12,14,19,13,9,3)(20,21,22)(30,31,32,34,33,35,36);(23,24,25,27,26,28,29)

Polycyclic presentation:

2,3^2,7^2,19|c^a=c^2,f^a=f^18,d^b=d^2,e^b=e^2,f^b=f^11

Conjugacy classes & character table

498 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#19150312, #45692382, #45692386, …
maximal normal subgroup ofD3×#19150312, #45692382, #45692386, …
maximal quotient ofC3⋊#26013845, C2×C3⋊#19150312

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 375);