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C3×D3553 #36319264

order21318
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3553
unambiguous semidirect productC11⋊(C3×D323)
unambiguous semidirect productC17⋊(C3×D209)

Splittings

Fitting, socle, HallC3×C11×C17×C19 ⋊ C2
derived, HallC11×C17×C19 ⋊ C2×C3
HallC3×C17×C19 ⋊ D11
HallC3×C11×C19 ⋊ D17
HallC3×C11×C17 ⋊ D19
HallC17×C19 ⋊ C3×D11
HallC11×C19 ⋊ C3×D17
HallC11×C17 ⋊ C3×D19
HallC3×C19 ⋊ D187
HallC3×C17 ⋊ D209
HallC3×C11 ⋊ D323
SylowC19 ⋊ C3×D187
SylowC17 ⋊ C3×D209
SylowC11 ⋊ C3×D323

Subgroups

subgroupG/H
center, hypercenterC3D3553
commutator, cosocle, hypocenterC11×C17×C19C2×C3
FrattiniC1G
Fitting, socleC3×C11×C17×C19C2
LCSG ▷ C11×C17×C19
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 10659

A minimal faithful permutation representation — 2 generators on 50 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(5,14)(6,13)(7,12)(8,11)(9,10)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

5334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21318, 9);