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C7×D17×C19⋊C3 #27214500

order13566
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D17×C19⋊C3
unambiguous semidirect productC17⋊(C2×C7×C19⋊C3)
unambiguous semidirect product(C19×D17)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C17×C19 ⋊ C2×C3
derived, HallC17×C19 ⋊ C2×C3×C7
HallC7×C17×C19⋊C3 ⋊ C2
HallC7×C19×D17 ⋊ C3
HallC17×C19⋊C3 ⋊ C2×C7
HallC19×D17 ⋊ C3×C7
HallC7×C19 ⋊ C3×D17
HallC7×C17 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×C7×D17
SylowC17 ⋊ C2×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D17×C19⋊C3
commutator, cosocle, hypocenterC17×C19C2×C3×C7
FrattiniC1G
Fitting, socleC7×C17×C19C2×C3
LCSG ▷ C17×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 2261

A minimal faithful permutation representation — 2 generators on 43 points:

(2,3,5)(4,7,8)(6,10,9)(11,15,13)(12,16,14)(17,19,18)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38,39,40,41,42,43);(1,2,4,8,13,18,15,3,6,11,16,5,9,14,7,12,17,19,10)(20,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×(C19⋊C3)⋊#595, C7×C19⋊C3×#595, C7×D17×D19⋊C3, …
maximal normal subgroup ofC7×(C19⋊C3)⋊#595, C7×C19⋊C3×#595, C7×D17×D19⋊C3, …
maximal quotient ofC7×C19⋊C3×Dic17, C2×C7×D17×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13566, 25);