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#117×C₃₀₇ #23754138

order	9824
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₀₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

#117×C₃₀₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₀₇	C₂²
commutator	C₂	C₂²×C₄×C₃₀₇
Frattini, cosocle	C₂²	C₂³×C₃₀₇
socle	C₂²×C₃₀₇	C₂³
prime radical	C₂³×C₃₀₇	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₀₇ ◁ G

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6140 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34087643, #34087646, #34087657, …
maximal subgroup of	H(3,ℤ/4)×C₃₀₇, #339×C₃₀₇, #344×C₃₀₇, …
maximal normal subgroup of	H(3,ℤ/4)×C₃₀₇, #339×C₃₀₇, #344×C₃₀₇, …
maximal quotient of	#376×C₃₀₇, C₄×C₂²⋊C₄×C₃₀₇, C₄×C₄⋊C₄×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 24);