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C₈²×C₁₇₉ #26037892

order	11456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 273408
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

C₈²×C₁₇₉

Subgroups

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

74 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11456 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₈×C₁₇₉⋊C₁₆, #37506917, #37506918, …
maximal subgroup of	C₈×C₁₆×C₁₇₉, #1311×C₁₇₉, #1312×C₁₇₉, …
maximal normal subgroup of	C₈×C₁₆×C₁₇₉, #1311×C₁₇₉, #1312×C₁₇₉, …
maximal quotient of	#1273×C₁₇₉, C₈×C₁₆×C₁₇₉, #1311×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 2);