C₉×Dic₁₀₇ #16838697

order	3852
isoclinism	isoclinic class of D₁₀₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×Dic₁₀₇
unambiguous semidirect product	C₁₀₇⋊(C₄×C₉)

Splittings

derived, Sylow	C₁₀₇ ⋊ C₄×C₉
Hall	C₉×C₁₀₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₀₇
commutator, hypocenter	C₁₀₇	C₄×C₉
Frattini	C₂×C₃	C₃×D₁₀₇
Fitting	C₂×C₉×C₁₀₇	C₂
socle, prime radical, cosocle	C₂×C₃×C₁₀₇	C₂×C₃
LCS	G ▷ C₁₀₇
UCS	C₁ ◁ C₂×C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 120
transitive degree	μ_t(G) = 3852

A minimal faithful permutation representation — 2 generators on 120 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);(10,12,11,13)(15,120)(16,119)(17,118)(18,117)(19,116)(20,115)(21,114)(22,113)(23,112)(24,111)(25,110)(26,109)(27,108)(28,107)(29,106)(30,105)(31,104)(32,103)(33,102)(34,101)(35,100)(36,99)(37,98)(38,97)(39,96)(40,95)(41,94)(42,93)(43,92)(44,91)(45,90)(46,89)(47,88)(48,87)(49,86)(50,85)(51,84)(52,83)(53,82)(54,81)(55,80)(56,79)(57,78)(58,77)(59,76)(60,75)(61,74)(62,73)(63,72)(64,71)(65,70)(66,69)(67,68)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₉×Dic₁₀₇, C₉×Dic₅₃₅, C₉×C₁₀₇⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₅×C₉×Dic₁₀₇, C₇×C₉×Dic₁₀₇
maximal quotient of	C₅×C₉×Dic₁₀₇, C₉×Dic₅₃₅, C₉×C₁₀₇⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3852, 3);

C9×Dic107 #16838697