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C₂×C₂²⋊C₄×C₃₇₃ #26045668

order	11936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇₃ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂²⋊C₄×C₃₇₃

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₇₃	C₂²
commutator	C₂	C₂²×C₄×C₃₇₃
Frattini, cosocle	C₂²	C₂³×C₃₇₃
prime radical	C₂⁴×C₃₇₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇₃ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7460 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#37559146, #37559188, #37559189, …
maximal subgroup of	#323×C₃₇₃, #342×C₃₇₃, C₄×C₂²⋊C₄×C₃₇₃, …
maximal normal subgroup of	#323×C₃₇₃, #342×C₃₇₃, C₄×C₂²⋊C₄×C₃₇₃, …
maximal quotient of	C₂×#95×C₃₇₃, C₄×C₂²⋊C₄×C₃₇₃, #379×C₃₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 22);