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C3⋊#19150286 #30660821

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

Aliases

unambiguous semidirect productC3⋊#19150286

Splittings

Fitting, socle, derivedC3×C72×C19 ⋊ C2×C3
HallC3×#14584115 ⋊ C2
HallC72×C19 ⋊ C3×D3
SylowC72 ⋊ D3×C19⋊C3
SylowC19 ⋊ C3⋊#64424

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:

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

Polycyclic presentation:

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

Conjugacy classes & character table

483 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#45692377, #45692385, D3×#19150286, …
maximal normal subgroup of#45692377, #45692385, D3×#19150286, …
maximal quotient ofC3⋊#26013819, C2×C3⋊#19150286

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 348);