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#322×C₁₇₉ #26037893

order	11456
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇₉ · Schur multiplier (H₂) = C₄

Aliases

#322×C₁₇₉

Subgroups

	subgroup	G/H
center	C₄²×C₁₇₉	C₂²
commutator	C₂	C₄×C₈×C₁₇₉
Frattini, cosocle	C₄²	C₂²×C₁₇₉
socle, prime radical	C₂²×C₁₇₉	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₇₉ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7160 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37506921, #37506977, #322×D₁₇₉, …
maximal subgroup of	#1313×C₁₇₉, #1336×C₁₇₉, C₂×#322×C₁₇₉, …
maximal normal subgroup of	#1313×C₁₇₉, #1336×C₁₇₉, C₂×#322×C₁₇₉, …
maximal quotient of	#1273×C₁₇₉, #1312×C₁₇₉, #1313×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 3);