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C₂²⋊C₁₆×C₁₆₇ #24922749

order	10688
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₁₆×C₁₆₇
unambiguous semidirect product	C₂²⋊(C₁₆×C₁₆₇)

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₆₇	C₂²
commutator	C₂	C₂×C₁₆×C₁₆₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₆₇
socle	C₂²×C₁₆₇	C₂×C₈
prime radical	C₂³×C₁₆₇	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₆₇ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6680 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36322061, #36322063, #36322077, …
maximal subgroup of	#1314×C₁₆₇, #1315×C₁₆₇, #1322×C₁₆₇, …
maximal normal subgroup of	#1314×C₁₆₇, #1315×C₁₆₇, #1322×C₁₆₇, …
maximal quotient of	#1314×C₁₆₇, #1322×C₁₆₇, D₄⋊C₁₆×C₁₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10688, 29);