C₄₃⋊C₃×C₁₃₇ #31799017

order	17673
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₃⋊C₃×C₁₃₇
unambiguous semidirect product	C₄₃⋊(C₃×C₁₃₇)
unambiguous semidirect product	(C₄₃×C₁₃₇)⋊C₃

Splittings

Fitting, socle, Hall	C₄₃×C₁₃₇ ⋊ C₃
derived, Sylow	C₄₃ ⋊ C₃×C₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃₇	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₄₃×C₁₃₇	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₁₃₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 180
transitive degree	μ_t(G) = 5891

A minimal faithful permutation representation — 2 generators on 180 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)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180);(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)

Conjugacy classes & character table

2329 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄₃⋊C₃×C₁₃₇, C₄₃⋊C₃×D₁₃₇, C₁₃₇×D₄₃⋊C₃, …
maximal normal subgroup of	C₂×C₄₃⋊C₃×C₁₃₇, C₄₃⋊C₃×D₁₃₇, C₁₃₇×D₄₃⋊C₃, …
maximal quotient of	C₂×C₄₃⋊C₃×C₁₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17673, 1);

C43⋊C3×C137 #31799017