Finite Group Databasebeta

← Prev (#30660831) Next (#30660833) →

C3⋊#19150297 #30660832

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

Aliases

unambiguous semidirect productC3⋊#19150297

Splittings

Fitting, socle, derivedC3×C72×C19 ⋊ C2×C3
HallC3×#14584116 ⋊ C2
HallC72×C19 ⋊ C3×D3
SylowC72 ⋊ D3×C19⋊C3
SylowC19 ⋊ C3⋊#64423

Subgroups

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

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 798

A minimal faithful permutation representation — 2 generators on 36 points:

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

Polycyclic presentation:

2,3^2,7^2,19|c^a=c^2,d^a=d^6,d^b=d^2,e^b=e^2,f^b=f^11

Conjugacy classes & character table

540 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#45692393, #45692401, D3×#19150297, …
maximal normal subgroup of#45692393, #45692401, D3×#19150297, …
maximal quotient ofC3⋊#26013830, C2×C3⋊#19150297

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 359);