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#350×C₁₃₇ #22576885

order	8768
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃₇ · Schur multiplier (H₂) = C₂

Aliases

#350×C₁₃₇

Subgroups

	subgroup	G/H
center	C₈×C₁₃₇	D₄
commutator	C₄	C₂×C₈×C₁₃₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₇
socle	C₂×C₁₃₇	C₂²⋊C₈
prime radical	#41×C₁₃₇	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3836 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#350×D₁₃₇, #31782415, #31782623, …
maximal subgroup of	C₂×#350×C₁₃₇, #2117×C₁₃₇, #2170×C₁₃₇, …
maximal normal subgroup of	C₂×#350×C₁₃₇, #2117×C₁₃₇, #2170×C₁₃₇, …
maximal quotient of	#1315×C₁₃₇, #1323×C₁₃₇, D₄⋊C₁₆×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 31);