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C₂³×C₈×C₁₇₉ #26038136

order	11456
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 7655424
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian	C₂³×C₈×C₁₇₉
multiplicative	(ℤ/34392)ˣ, (ℤ/34464)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₁₇₉
socle, prime radical	C₂⁴×C₁₇₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

338 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	C₂×#26038193, #37508696, C₂×#26038202, …
maximal subgroup of	C₂×#336×C₁₇₉, #1729×C₁₇₉, C₂×#340×C₁₇₉, …
maximal normal subgroup of	C₂×#336×C₁₇₉, #1729×C₁₇₉, C₂×#340×C₁₇₉, …
maximal quotient of	C₂²×C₄×C₈×C₁₇₉, C₂²×C₂²⋊C₈×C₁₇₉, C₂²×C₄⋊C₈×C₁₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11456, 246);