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C3⋊#19150284 #30660819

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

Aliases

unambiguous semidirect productC3⋊#19150284

Splittings

Fitting, socle, derivedC3×C72×C19 ⋊ C2×C3
HallC3×#14584115 ⋊ C2
HallC72×C19 ⋊ C3×D3
SylowC72 ⋊ C3⋊(D19⋊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:

(2,6,7,3,4,8)(5,14,11,9,10,16)(12,17,19,18,15,13)(21,22)(24,27,28,25,26,29)(31,34,35,32,33,36);(1,2,5,11,17,14,18,4,8,13,19,7,6,12,10,15,16,9,3)(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,f^a=f^18,d^b=d^2,e^b=e^2,f^b=f^7

Conjugacy classes & character table

474 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#45692377, #45692381, D3×#19150284, …
maximal normal subgroup of#45692377, #45692381, D3×#19150284, …
maximal quotient ofC3⋊#26013817, C2×C3⋊#19150284

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 346);