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#95×C₂₂₇ #20300144

order	7264
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₂₇ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₂₂₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₂₇	C₂²
commutator	C₂	C₄²×C₂₂₇
Frattini, cosocle	C₂³	C₂²×C₂₂₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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	#28408765, #28408768, #95×D₂₂₇, …
maximal subgroup of	#327×C₂₂₇, #328×C₂₂₇, C₂×#95×C₂₂₇, …
maximal normal subgroup of	#327×C₂₂₇, #328×C₂₂₇, C₂×#95×C₂₂₇, …
maximal quotient of	#336×C₂₂₇, H(3,ℤ/4)×C₂₂₇, #338×C₂₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7264, 2);