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#117×C₃₁₇ #23778658

order	10144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₃₁₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₁₇	C₂²
commutator	C₂	C₂²×C₄×C₃₁₇
Frattini, cosocle	C₂²	C₂³×C₃₁₇
socle	C₂²×C₃₁₇	C₂³
prime radical	C₂³×C₃₁₇	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁₇ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6340 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35202979, #35202982, #35202993, …
maximal subgroup of	H(3,ℤ/4)×C₃₁₇, #339×C₃₁₇, #344×C₃₁₇, …
maximal normal subgroup of	H(3,ℤ/4)×C₃₁₇, #339×C₃₁₇, #344×C₃₁₇, …
maximal quotient of	#376×C₃₁₇, C₄×C₂²⋊C₄×C₃₁₇, C₄×C₄⋊C₄×C₃₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10144, 24);