C₃×C₁₃⋊D₂₂₁ #31771963

order	17238
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₃×C₁₃⋊D₂₂₁
unambiguous semidirect product	C₁₇⋊(C₃×C₁₃⋊D₁₃)

Splittings

Fitting, socle, Hall	C₃×C₁₃²×C₁₇ ⋊ C₂
derived, Hall	C₁₃²×C₁₇ ⋊ C₂×C₃
Hall	C₃×C₁₃² ⋊ D₁₇
Sylow	C₁₃² ⋊ C₃×D₁₇
Hall	C₃×C₁₇ ⋊ C₁₃⋊D₁₃
Sylow	C₁₇ ⋊ C₃×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊D₂₂₁
commutator, cosocle, hypocenter	C₁₃²×C₁₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₁₇	C₂
LCS	G ▷ C₁₃²×C₁₇
UCS	C₁ ◁ C₃

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 8619

A minimal faithful permutation representation — 3 generators on 46 points:

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

Conjugacy classes & character table

4314 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₁₃×D₂₂₁, C₃×D₁₇×C₁₃⋊D₁₃, C₃×#26040109, …
maximal normal subgroup of	C₃×D₁₃×D₂₂₁, C₃×D₁₇×C₁₃⋊D₁₃, C₃×#26040109, …
maximal quotient of	C₃×#26040095, C₂×C₃×C₁₃⋊D₂₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17238, 42);

C3×C13⋊D221 #31771963