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C₂×#405×C₈₉ #26017346

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

Aliases

C₂×#405×C₈₉

Subgroups

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

592 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	#36444956, #36444960, #36447289, …
maximal subgroup of	C₈₉×#8156, C₈₉×#8157, C₈₉×#8601, …
maximal normal subgroup of	C₈₉×#8156, C₈₉×#8157, C₈₉×#8601, …
maximal quotient of	C₂×C₈×M₁₆×C₈₉, C₂×C₈₉×#1450, C₂×C₈₉×#1451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1604);