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#117×C₂₂₇ #20300166

order	7264
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₂₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₂₂₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₂₇	C₂²
commutator	C₂	C₂²×C₄×C₂₂₇
Frattini, cosocle	C₂²	C₂³×C₂₂₇
socle	C₂²×C₂₂₇	C₂³
prime radical	C₂³×C₂₂₇	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₂₇ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4540 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28408788, #28408791, #28408802, …
maximal subgroup of	H(3,ℤ/4)×C₂₂₇, #339×C₂₂₇, #344×C₂₂₇, …
maximal normal subgroup of	H(3,ℤ/4)×C₂₂₇, #339×C₂₂₇, #344×C₂₂₇, …
maximal quotient of	#376×C₂₂₇, C₄×C₂²⋊C₄×C₂₂₇, C₄×C₄⋊C₄×C₂₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7264, 24);