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#328×C₁₃₇ #22576863

order	8768
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₇ · Schur multiplier (H₂) = C₂

Aliases

#328×C₁₃₇

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₁₃₇
Frattini, cosocle	C₂²×C₄	C₂²×C₁₃₇
prime radical	C₂³×C₁₃₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₂²×C₄×C₁₃₇ ◁ G

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2603 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#328×D₁₃₇, #31779274, #31779279, …
maximal subgroup of	C₂×#328×C₁₃₇, #1500×C₁₃₇, #1501×C₁₃₇, …
maximal normal subgroup of	C₂×#328×C₁₃₇, #1500×C₁₃₇, #1501×C₁₃₇, …
maximal quotient of	#1271×C₁₃₇, #1272×C₁₃₇, #1294×C₁₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 9);