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C₂×#431×C₆₇ #22557348

order	8576
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₆₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×#431×C₆₇

Subgroups

	subgroup	G/H
center	C₂×C₄²×C₆₇	C₂²
commutator	C₂	C₂³×C₈×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁴×C₆₇
socle	C₂³×C₆₇	C₂²×C₄
prime radical	C₂⁴×C₆₇	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₆₇ ◁ G

528 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	#30745214, #30745217, #30745219, …
maximal subgroup of	C₆₇×#7848, C₆₇×#7849, C₆₇×#7850, …
maximal normal subgroup of	C₆₇×#7848, C₆₇×#7849, C₆₇×#7850, …
maximal quotient of	C₂×C₆₇×#1744, C₂×C₄×C₂²⋊C₈×C₆₇, C₂×C₄×C₄⋊C₈×C₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 1649);