C₃×D₁₇×C₄₃ #17984191

order	4386
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₁₇×C₄₃
unambiguous semidirect product	C₁₇⋊(C₂×C₃×C₄₃)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₄₃ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₃×C₄₃
Hall	C₁₇×C₄₃ ⋊ C₂×C₃
Hall	C₃×C₁₇ ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₃	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₄₃	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₄₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 2193

A minimal faithful permutation representation — 2 generators on 63 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63);(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)

Conjugacy classes & character table

1290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×C₄₃, D₁₇×C₄₃⋊C₉, C₃×D₁₇×C₄₃⋊C₃, …
maximal normal subgroup of	C₉×D₁₇×C₄₃, D₁₇×C₄₃⋊C₉, C₃×D₁₇×C₄₃⋊C₃, …
maximal quotient of	C₉×D₁₇×C₄₃, C₃×C₄₃×D₅₁, C₃²×D₁₇×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4386, 4);

C3×D17×C43 #17984191