C₂²⋊C₉×C₄₁ #13093272

order	1476
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₉×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂²⋊C₉×C₄₁
unambiguous semidirect product	C₂²⋊(C₉×C₄₁)
unambiguous semidirect product	(C₂²×C₄₁)⋊C₉

Splittings

derived, Sylow	C₂² ⋊ C₉×C₄₁
Hall	C₂²×C₄₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₁	A₄
commutator, hypocenter	C₂²	C₉×C₄₁
Frattini	C₃	A₄×C₄₁
Fitting, socle, prime radical	C₂²×C₃×C₄₁	C₃
cosocle	C₂²×C₃	C₃×C₄₁
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₄₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 54
transitive degree	μ_t(G) = 738

A minimal faithful permutation representation — 2 generators on 54 points:

(2,3,4)(5,6,8,7,9,11,10,12,13)(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);(1,4)(2,3)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁×C₂²⋊C₉×C₄₁, C₁₃×C₂²⋊C₉×C₄₁, C₄₁×C₂²⋊(C₁₃⋊C₉), …
maximal normal subgroup of	C₁₁×C₂²⋊C₉×C₄₁, C₁₃×C₂²⋊C₉×C₄₁, C₁₇×C₂²⋊C₉×C₄₁, …
maximal quotient of	C₁₁×C₂²⋊C₉×C₄₁, C₁₃×C₂²⋊C₉×C₄₁, C₄₁×C₂²⋊(C₁₃⋊C₉), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1476, 8);

C22⋊C9×C41 #13093272