Finite Group Databasebeta

← Prev (#26016730) Next (#26016732) →

C₂×M₆₄×C₈₉ #26016731

order	11392
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₈₉ · Schur multiplier (H₂) = C₂²

Aliases

C₂×M₆₄×C₈₉

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₈₉	C₂²
commutator	C₂	C₂²×C₁₆×C₈₉
Frattini, cosocle	C₁₆	C₂³×C₈₉
socle	C₂²×C₈₉	C₂×C₁₆
prime radical	C₂³×C₈₉	C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₈₉ ◁ G

112 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	#36442116, #36442118, #36442120, …
maximal subgroup of	C₈₉×#7466, C₈₉×#7467, C₈₉×#7468, …
maximal normal subgroup of	C₈₉×#7466, C₈₉×#7467, C₈₉×#7468, …
maximal quotient of	C₂×C₈₉×#1397, C₄×M₆₄×C₈₉, C₂×C₈₉×C₂²⋊C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 989);