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C₂×C₄×SD₁₆×C₈₉ #26017411

order	11392
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₈₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₄×SD₁₆×C₈₉

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₈₉	D₄
commutator	C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
socle	C₂³×C₈₉	C₂×D₄
prime radical	C₂²×D₄×C₈₉	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

552 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4984 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36448991, #36449012, #36449019, …
maximal subgroup of	C₈₉×#8945, C₈₉×#8948, C₈₉×#8949, …
maximal normal subgroup of	C₈₉×#8945, C₈₉×#8948, C₈₉×#8949, …
maximal quotient of	C₂×C₈×SD₁₆×C₈₉, C₂×C₈₉×#1583, C₂×C₈₉×#1582, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1669);