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#117×C₃₃₇ #24924837

order	10784
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₃₃₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₃₇	C₂²
commutator	C₂	C₂²×C₄×C₃₃₇
Frattini, cosocle	C₂²	C₂³×C₃₃₇
socle	C₂²×C₃₃₇	C₂³
prime radical	C₂³×C₃₃₇	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₃₇ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6740 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#36341061, #36341064, #36341075, …
maximal subgroup of	H(3,ℤ/4)×C₃₃₇, #339×C₃₃₇, #344×C₃₃₇, …
maximal normal subgroup of	H(3,ℤ/4)×C₃₃₇, #339×C₃₃₇, #344×C₃₃₇, …
maximal quotient of	#376×C₃₃₇, C₄×C₂²⋊C₄×C₃₃₇, C₄×C₄⋊C₄×C₃₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10784, 24);