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C19⋊C3×#10596885 #45691981

order33516
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC19⋊C3×#10596885

Splittings

Fitting, socle, HallC72×C19 ⋊ C3×Dic3
derivedC19×#3862 ⋊ C3×C4
HallC19⋊C3×#3862 ⋊ C4
SylowC72 ⋊ Dic3×C19⋊C3
SylowC19 ⋊ C3×#10596885

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterC19×#3862C3×C4
Fitting, socleC72×C19C3×Dic3
prime radicalC19⋊C3×#64425C2
cosocleC19×#64425C2×C3
LCSG ▷ C19×#3862
UCSC1

88 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:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 779);