Finite Group Databasebeta

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#95×C₃₀₇ #23754116

order	9824
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄²×C₃₀₇ · Schur multiplier (H₂) = C₂³

Aliases

#95×C₃₀₇

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₀₇	C₂²
commutator	C₂	C₄²×C₃₀₇
Frattini, cosocle	C₂³	C₂²×C₃₀₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×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	#34087620, #34087623, #95×D₃₀₇, …
maximal subgroup of	#327×C₃₀₇, #328×C₃₀₇, C₂×#95×C₃₀₇, …
maximal normal subgroup of	#327×C₃₀₇, #328×C₃₀₇, C₂×#95×C₃₀₇, …
maximal quotient of	#336×C₃₀₇, H(3,ℤ/4)×C₃₀₇, #338×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 2);