C₃×C₃₁×D₁₉ #16812959

order	3534
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₃₁×D₁₉

Splittings

Fitting, socle, Hall	C₃×C₁₉×C₃₁ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₃×C₃₁
Hall	C₁₉×C₃₁ ⋊ C₂×C₃
Hall	C₃×C₁₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₃₁	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1767

A minimal faithful permutation representation — 2 generators on 53 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

1023 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×C₃₁×D₁₉, C₃×C₃₁×D₉₅, C₃×D₁₉×ΓL(1,𝔽₃₂), …
maximal normal subgroup of	C₃×C₅×C₃₁×D₁₉, C₃×D₁₉×ΓL(1,𝔽₃₂), C₃×C₇×C₃₁×D₁₉
maximal quotient of	C₃×C₅×C₃₁×D₁₉, C₃×C₃₁×D₉₅, C₃×C₇×C₃₁×D₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3534, 7);

C3×C31×D19 #16812959