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C₄×AGL(1,ℤ/8)×C₈₉ #26017418

order	11392
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₈₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₄×AGL(1,ℤ/8)×C₈₉

Subgroups

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂×D₄
commutator	C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₈₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

548 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	#36449054, #36449068, #36449897, …
maximal subgroup of	C₈₉×#8954, C₈₉×#8956, C₈₉×#9095, …
maximal normal subgroup of	C₈₉×#8954, C₈₉×#8956, C₈₉×#9095, …
maximal quotient of	C₈×AGL(1,ℤ/8)×C₈₉, C₈₉×#17869, C₈₉×#17871, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1676);