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C₂×#383×C₈₉ #26016756

order	11392
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₈₉ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×#383×C₈₉

Subgroups

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

624 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	#36444052, C₂×#26018116, #36444283, …
maximal subgroup of	C₈₉×#7916, C₂×C₈₉×#1288, C₈₉×#7975, …
maximal normal subgroup of	C₈₉×#7916, C₂×C₈₉×#1288, C₈₉×#7975, …
maximal quotient of	C₂×C₈₉×#1434, C₄×#383×C₈₉, C₂×C₈₉×#1443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11392, 1014);