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#108×C₃₀₇ #23754129

order	9824
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₀₇ · Schur multiplier (H₂) = C₁

Aliases

#108×C₃₀₇

Subgroups

	subgroup	G/H
center	C₄×C₃₀₇	D₄
commutator	C₄	C₂×C₄×C₃₀₇
Frattini, cosocle	C₂×C₄	C₂²×C₃₀₇
socle	C₂×C₃₀₇	C₄⋊C₄
prime radical	C₂²×C₃₀₇	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₀₇ ◁ C₂×C₄×C₃₀₇ ◁ G

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4298 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#34087693, #34087699, #34087702, …
maximal subgroup of	#359×C₃₀₇, #361×C₃₀₇, #362×C₃₀₇, …
maximal normal subgroup of	#359×C₃₀₇, #361×C₃₀₇, #362×C₃₀₇, …
maximal quotient of	#334×C₃₀₇, #335×C₃₀₇, #341×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 15);