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C₄×Q₃₂×C₈₉ #26016648

order	11392
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₉ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Q₃₂×C₈₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₈₉	D₈
commutator	C₈	C₂²×C₄×C₈₉
Frattini, cosocle	C₂×C₈	C₂³×C₈₉
socle, prime radical	C₂²×C₈₉	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₄²×C₈₉ ◁ C₄×C₈×C₈₉ ◁ G

150 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3916 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36441881, #36441887, Q₃₂×#10623494, …
maximal subgroup of	C₈₉×#7384, C₈₉×#7386, C₈×Q₃₂×C₈₉, …
maximal normal subgroup of	C₈₉×#7384, C₈₉×#7386, C₈×Q₃₂×C₈₉, …
maximal quotient of	C₈×Q₃₂×C₈₉, C₈₉×#12072, C₈₉×#12083, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 906);