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C₄×#131×C₈₉ #26017348

order	11392
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₈₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₄×#131×C₈₉

Subgroups

	subgroup	G/H
center	C₄×C₈×C₈₉	C₂²
commutator	C₂	C₂²×C₄²×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂³×C₄
prime radical	C₂×#41×C₈₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₈₉ ◁ G

572 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7120 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36445100, #36445105, #36445110, …
maximal subgroup of	C₈₉×#8184, C₈₉×#8185, C₈₉×#8186, …
maximal normal subgroup of	C₈₉×#8184, C₈₉×#8185, C₈₉×#8186, …
maximal quotient of	C₈×#131×C₈₉, C₈₉×#17320, C₈₉×#17328, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1606);