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C2×#30660648 #45692170

order33516
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×#30660648

Splittings

Fitting, socleC2×C72×C19 ⋊ C2×C9
derived, HallC72×C19 ⋊ C22×C9
Hall#22552719 ⋊ C22
HallC2×C7⋊D133 ⋊ C9
SylowC72 ⋊ C2×AGL(1,𝔽19)
SylowC19 ⋊ C2×#11725077

Subgroups

subgroupG/H
center, hypercenterC2#30660648
commutator, hypocenterC72×C19C22×C9
FrattiniC1G
Fitting, socleC2×C72×C19C2×C9
prime radicalC2×(C19⋊C3)⋊(C7⋊D7)C3
cosocleC72×C19⋊C3C22×C3
LCSG ▷ C72×C19
UCSC1 ◁ C2

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1862

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 968);