C₃²×Dic₄₁ #13093277

order	1476
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₃²×Dic₄₁

Splittings

derived, Sylow	C₄₁ ⋊ C₃²×C₄
Hall	C₃²×C₄₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₄₁
commutator, hypocenter	C₄₁	C₃²×C₄
Frattini	C₂	C₃²×D₄₁
Fitting, socle, prime radical	C₂×C₃²×C₄₁	C₂
cosocle	C₂×C₄₁	C₂×C₃²
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₃²

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1476

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3)(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);(4,5,6)(7,9,8,10)(12,51)(13,50)(14,49)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃²×C₁₁×Dic₄₁, C₃²×Dic₄₅₁, C₃×Dic₅₃₃⋊C₃, …
maximal normal subgroup of	C₃²×C₁₁×Dic₄₁, C₃²×C₁₃×Dic₄₁, C₃²×C₁₇×Dic₄₁, …
maximal quotient of	C₃²×C₁₁×Dic₄₁, C₃²×Dic₄₅₁, C₃×Dic₅₃₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 13);

C32×Dic41 #13093277