C₁₉×D₁₂₁ #17987147

order	4598
isoclinism	isoclinic class of D₁₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₁₂₁
unambiguous semidirect product	C₁₂₁⋊(C₂×C₁₉)

Splittings

Fitting, Hall	C₁₉×C₁₂₁ ⋊ C₂
derived, Sylow	C₁₂₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₁₂₁
commutator, cosocle, hypocenter	C₁₂₁	C₂×C₁₉
Frattini	C₁₁	C₁₉×D₁₁
Fitting	C₁₉×C₁₂₁	C₂
socle	C₁₁×C₁₉	D₁₁
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₁₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 140
transitive degree	μ_t(G) = 2299

A minimal faithful permutation representation — 2 generators on 140 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140);(21,140)(22,139)(23,138)(24,137)(25,136)(26,135)(27,134)(28,133)(29,132)(30,131)(31,130)(32,129)(33,128)(34,127)(35,126)(36,125)(37,124)(38,123)(39,122)(40,121)(41,120)(42,119)(43,118)(44,117)(45,116)(46,115)(47,114)(48,113)(49,112)(50,111)(51,110)(52,109)(53,108)(54,107)(55,106)(56,105)(57,104)(58,103)(59,102)(60,101)(61,100)(62,99)(63,98)(64,97)(65,96)(66,95)(67,94)(68,93)(69,92)(70,91)(71,90)(72,89)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉⋊C₃×D₁₂₁, C₃×C₁₉×D₁₂₁, C₁₉×D₃₆₃, …
maximal normal subgroup of	C₁₉⋊C₃×D₁₂₁, C₃×C₁₉×D₁₂₁, C₅×C₁₉×D₁₂₁, …
maximal quotient of	C₃×C₁₉×D₁₂₁, C₁₉×D₃₆₃, C₅×C₁₉×D₁₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4598, 2);

C19×D121 #17987147