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C₉²×#41 #13047510

order	1296
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉² · Schur multiplier (H₂) = C₂²×C₉

Aliases

C₉²×#41

Subgroups

	subgroup	G/H
center	C₄×C₉²	C₂²
commutator	C₂	C₂³×C₉²
Frattini, socle, cosocle	C₂×C₃²	C₂³×C₃²
prime radical	C₃²×#41	C₃²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉² ◁ G

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 648

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3,4,5,6,7,8,9)(19,20)(21,24)(22,23)(25,26);(10,11,12,13,14,15,16,17,18)(20,23)(24,26);(19,21,22,25)(20,24,23,26)

Conjugacy classes & character table

810 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#41×C₉⋊D₉, #72252666
maximal subgroup of	C₉²×AGL(1,ℤ/8), #41×C₉⋊D₉, #72252666, …
maximal normal subgroup of	C₉²×AGL(1,ℤ/8), #41×C₉⋊D₉, #72252666, …
maximal quotient of	C₄×D₄×C₉², C₂×C₉²×#41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1228);