C₉×Dic₄₁ #13093266

order	1476
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×Dic₄₁

Splittings

derived, Sylow	C₄₁ ⋊ C₄×C₉
Hall	C₉×C₄₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₄₁
commutator, hypocenter	C₄₁	C₄×C₉
Frattini	C₂×C₃	C₃×D₄₁
Fitting	C₂×C₉×C₄₁	C₂
socle, prime radical, cosocle	C₂×C₃×C₄₁	C₂×C₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 1476

A minimal faithful permutation representation — 2 generators on 54 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);(10,12,11,13)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×C₁₁×Dic₄₁, C₉×Dic₄₅₁, C₉×C₁₃×Dic₄₁, …
maximal normal subgroup of	C₉×C₁₁×Dic₄₁, C₉×C₁₃×Dic₄₁, C₉×C₁₇×Dic₄₁, …
maximal quotient of	C₉×C₁₁×Dic₄₁, C₉×Dic₄₅₁, C₉×C₁₃×Dic₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 2);

C9×Dic41 #13093266