C₃×D₁₇×C₄₃⋊C₃ #27190482

order	13158
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×D₁₇×C₄₃⋊C₃
unambiguous semidirect product	C₁₇⋊(C₂×C₃×C₄₃⋊C₃)
unambiguous semidirect product	(D₁₇×C₄₃)⋊C₃²
unambiguous semidirect product	(C₃×D₁₇×C₄₃)⋊C₃

Splittings

Fitting, socle	C₃×C₁₇×C₄₃ ⋊ C₂×C₃
derived, Hall	C₁₇×C₄₃ ⋊ C₂×C₃²
Hall	C₃×C₁₇×C₄₃⋊C₃ ⋊ C₂
Hall	D₁₇×C₄₃ ⋊ C₃²
Sylow	C₄₃ ⋊ C₃²×D₁₇
Sylow	C₁₇ ⋊ C₂×C₃×C₄₃⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₁₇×C₄₃⋊C₃
commutator, cosocle, hypocenter	C₁₇×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₄₃	C₂×C₃
LCS	G ▷ C₁₇×C₄₃
UCS	C₁ ◁ C₃

48 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×(C₄₃⋊C₃)⋊#595, C₃×#595×C₄₃⋊C₃, C₃×D₁₇×D₄₃⋊C₃, …
maximal normal subgroup of	C₃×(C₄₃⋊C₃)⋊#595, C₃×#595×C₄₃⋊C₃, C₃×D₁₇×D₄₃⋊C₃, …
maximal quotient of	C₃×Dic₁₇×C₄₃⋊C₃, C₂×C₃×D₁₇×C₄₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 16);

C3×D17×C43⋊C3 #27190482