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#357×C₁₃₇ #22576892

order	8768
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₇ · Schur multiplier (H₂) = C₂²

Aliases

#357×C₁₃₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₇	D₈
commutator	C₈	C₂×C₄×C₁₃₇
Frattini, cosocle	C₂×C₈	C₂²×C₁₃₇
prime radical	C₂×D₈×C₁₃₇	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂×C₄×C₁₃₇ ◁ C₂×C₈×C₁₃₇ ◁ G

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3014 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#357×D₁₃₇, #31782493, #31782498, …
maximal subgroup of	C₂×#357×C₁₃₇, #2138×C₁₃₇, #2139×C₁₃₇, …
maximal normal subgroup of	C₂×#357×C₁₃₇, #2138×C₁₃₇, #2139×C₁₃₇, …
maximal quotient of	#1331×C₁₃₇, #1347×C₁₃₇, #1361×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 38);