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M₃₂×C₃₀₇ #23754131

order	9824
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₀₇ · Schur multiplier (H₂) = C₁

Aliases

M₃₂×C₃₀₇

Subgroups

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

26 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	#34087664, #34087668, #34087672, …
maximal subgroup of	#347×C₃₀₇, #349×C₃₀₇, #350×C₃₀₇, …
maximal normal subgroup of	#347×C₃₀₇, #349×C₃₀₇, #350×C₃₀₇, …
maximal quotient of	#346×C₃₀₇, C₂²⋊C₁₆×C₃₀₇, C₄⋊C₁₆×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 17);