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C₈₉×#2922 #26017396

order	11392
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₈₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

Subgroups

	subgroup	G/H
center	C₄²×C₈₉	C₂³
commutator	C₂²	C₂³×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂³×C₄
prime radical	C₂×#41×C₈₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₈₉ ◁ G

400 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	#36445117, #36445122, #36445127, …
maximal subgroup of	C₈₉×#8187, C₈₉×#8188, C₈₉×#8189, …
maximal normal subgroup of	C₈₉×#8187, C₈₉×#8188, C₈₉×#8189, …
maximal quotient of	C₈₉×#20366, C₄×#408×C₈₉, C₄×#424×C₈₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1654);