Finite Group Databasebeta

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C₄×#117×C₆₇ #22556701

order	8576
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₆₇ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

C₄×#117×C₆₇

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₆₇	C₂²
commutator	C₂	C₂²×C₄²×C₆₇
Frattini, cosocle	C₂³	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂⁴
prime radical	C₂⁴×C₆₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₆₇ ◁ G

752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5360 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#30745230, #30745236, #30745270, …
maximal subgroup of	C₆₇×#7854, C₆₇×#7856, C₆₇×#7866, …
maximal normal subgroup of	C₆₇×#7854, C₆₇×#7856, C₆₇×#7866, …
maximal quotient of	C₄×#376×C₆₇, C₄²×C₂²⋊C₄×C₆₇, C₄²×C₄⋊C₄×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 1002);