Finite Group Databasebeta

← Prev (#30660730) Next (#30660732) →

C19⋊C3×#64418 #30660731

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

Aliases

direct productC19⋊C3×#64418

Splittings

Fitting, socle, HallC72×C19 ⋊ C3×D3
derivedC19×#3862 ⋊ C2×C3
HallC19⋊C3×#3862 ⋊ C2
SylowC72 ⋊ D3×C19⋊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:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×#64418, #45691988, C19⋊C3×#64418⋊C2, …
maximal normal subgroup ofD19⋊C3×#64418, #45691988, C19⋊C3×#64418⋊C2, …
maximal quotient ofC19⋊C3×#10596868, C2×C19⋊C3×#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 258);