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C2×C3×(C19⋊C3)⋊(C7⋊D7) #45692601

order33516
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C3×(C19⋊C3)⋊(C7⋊D7)
unambiguous semidirect product(C2×C19⋊C3)⋊(C3×C7⋊D7)

Splittings

Fitting, socleC2×C3×C72×C19 ⋊ C2×C3
derived, HallC72×C19 ⋊ C22×C32
HallC3×C72×C19⋊C3 ⋊ C22
HallC2×C7⋊D133 ⋊ C32
HallC3×C19⋊C3 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C3×D19⋊C3
SylowC19 ⋊ C2×C32×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3(C19⋊C3)⋊(C7⋊D7)
commutator, cosocle, hypocenterC72×C19C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C19C2×C3
LCSG ▷ C72×C19
UCSC1 ◁ C2×C3

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 5586

A minimal faithful permutation representation — 3 generators on 38 points:

(7,8)(9,10)(11,12)(14,15)(16,17)(18,19)(21,25,26,22,23,27)(24,33,30,28,29,35)(31,36,38,37,34,32);(1,2)(3,4,5)(13,14,16,18,19,17,15)(20,21,24,30,36,33,37,23,27,32,38,26,25,31,29,34,35,28,22);(6,7,9,11,12,10,8)

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 1399);