Finite Group Databasebeta

← Prev (#22576864) Next (#22576866) →

#330×C₁₃₇ #22576865

order	8768
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃₇ · Schur multiplier (H₂) = C₁

Aliases

#330×C₁₃₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₁₃₇
Frattini, cosocle	C₄²	C₂²×C₁₃₇
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₇ ◁ C₄²×C₁₃₇ ◁ G

60 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	#330×D₁₃₇, #31779376, #31779382, …
maximal subgroup of	C₂×#330×C₁₃₇, #1524×C₁₃₇, #1526×C₁₃₇, …
maximal normal subgroup of	C₂×#330×C₁₃₇, #1524×C₁₃₇, #1526×C₁₃₇, …
maximal quotient of	#1271×C₁₃₇, #1295×C₁₃₇, C₂×#330×C₁₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 11);