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#131×C₃₀₇ #23754152

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

Aliases

#131×C₃₀₇

Subgroups

	subgroup	G/H
center	C₈×C₃₀₇	C₂²
commutator	C₂	C₂²×C₄×C₃₀₇
Frattini, cosocle	C₄	C₂³×C₃₀₇
socle	C₂×C₃₀₇	C₂²×C₄
prime radical	#41×C₃₀₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₀₇ ◁ G

62 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	#34087671, #34088002, #34088007, …
maximal subgroup of	#350×C₃₀₇, #443×C₃₀₇, #444×C₃₀₇, …
maximal normal subgroup of	#350×C₃₀₇, #443×C₃₀₇, #444×C₃₀₇, …
maximal quotient of	#405×C₃₀₇, #408×C₃₀₇, #424×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 38);