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C₄²×Q₈×C₆₇ #22556703

order	8576
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₆₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₄²×Q₈×C₆₇

Subgroups

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

684 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	C₄×Q₈⋊(C₆₇⋊C₈), #30746438, #30746448, …
maximal subgroup of	C₄×Q₈⋊C₈×C₆₇, C₆₇×#8171, C₆₇×#8173, …
maximal normal subgroup of	C₄×Q₈⋊C₈×C₆₇, C₆₇×#8171, C₆₇×#8173, …
maximal quotient of	C₄²×C₄⋊C₄×C₆₇, C₄×#387×C₆₇, C₄×#389×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 1004);