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#338×C₁₇₉ #26037909

order	11456
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇₉ · Schur multiplier (H₂) = C₂²

Aliases

#338×C₁₇₉

Subgroups

	subgroup	G/H
center	C₄×C₁₇₉	C₄²
commutator	C₄	C₄²×C₁₇₉
Frattini, cosocle	C₂²×C₄	C₂²×C₁₇₉
socle	C₂×C₁₇₉	#95
prime radical	C₂³×C₁₇₉	Q₈
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇₉ ◁ G

86 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3938 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37506990, #37506993, #338×D₁₇₉, …
maximal subgroup of	#1341×C₁₇₉, #1342×C₁₇₉, C₂×#338×C₁₇₉, …
maximal normal subgroup of	#1341×C₁₇₉, #1342×C₁₇₉, C₂×#338×C₁₇₉, …
maximal quotient of	#1275×C₁₇₉, #1291×C₁₇₉, #1292×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 19);