#473×D₁₀₃ #27204853

order	13184
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

#473×D₁₀₃

Splittings

Fitting	#473×C₁₀₃ ⋊ C₂
Sylow	C₁₀₃ ⋊ C₂×#473

Subgroups

	subgroup	G/H
center	C₂	#121×D₁₀₃
commutator, cosocle	C₂×C₄×C₁₀₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₃
Fitting	#473×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×#121
prime radical	#41×D₁₀₃	C₂²
hypercenter	#473	D₁₀₃
hypocenter	C₁₀₃	C₂×#473
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #473

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 4 generators on 135 points:

(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)(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(104,107)(105,112)(106,117)(108,122)(109,124)(110,123)(111,125)(113,121)(114,129)(115,128)(116,130)(118,132)(119,134)(120,133)(126,135)(127,131);(104,106,109,119,110,120,108,118)(105,111,114,126,115,127,113,116)(107,117,124,134,123,133,122,132)(112,125,129,135,128,131,121,130);(104,105,110,115)(106,116,120,126)(107,121,123,129)(108,114,109,113)(111,119,127,118)(112,124,128,122)(117,131,133,125)(130,134,135,132)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 14219);

#473×D103 #27204853