Dic₉×C₄₁ #13093265

order	1476
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₉×C₄₁
unambiguous semidirect product	C₉⋊(C₄×C₄₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₁	D₉
commutator, hypocenter	C₉	C₄×C₄₁
Frattini	C₂×C₃	D₃×C₄₁
Fitting	C₂×C₉×C₄₁	C₂
socle, prime radical	C₂×C₃×C₄₁	D₃
cosocle	C₂×C₉	C₂×C₄₁
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₄₁

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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁×Dic₉×C₄₁, C₄₁×Dic₉₉, C₁₃×Dic₉×C₄₁, …
maximal normal subgroup of	C₁₁×Dic₉×C₄₁, C₁₃×Dic₉×C₄₁, C₁₇×Dic₉×C₄₁, …
maximal quotient of	C₁₁×Dic₉×C₄₁, C₄₁×Dic₉₉, C₁₃×Dic₉×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 1);

Dic9×C41 #13093265