#27204050

order	13184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Fitting	C₂×#104×C₁₀₃ ⋊ C₂
Sylow	C₁₀₃ ⋊ #2956

Subgroups

	subgroup	G/H
center	C₄	C₂×D₄×D₁₀₃
commutator	C₄×C₁₀₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₃
Fitting	C₂×#104×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×C₄×D₄
prime radical	#20268589	C₂
cosocle	C₂×C₄×C₁₀₃	C₂⁴
hypercenter	C₂×#104	D₁₀₃
hypocenter	C₁₀₃	#2956
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#104

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 1648

A minimal faithful permutation representation — 4 generators on 119 points:

(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)(107,115)(110,114)(116,119)(117,118);(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)(104,107,108,116,109,115,113,119)(105,110,112,118,106,114,111,117);(104,106)(105,109)(107,114)(108,111)(110,115)(112,113)(116,117)(118,119);(104,105,108,112,109,106,113,111)(107,110,116,118,115,114,119,117)

Polycyclic presentation:

2^7,103|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,e^b=eg,d^c=dg,h^c=h^102

Conjugacy classes & character table

1472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13184, 13416);