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C₂×C₂²⋊C₄×C₃₀₇ #23754136

order	9824
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₀₇ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×C₂²⋊C₄×C₃₀₇

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃₀₇	C₂²
commutator	C₂	C₂²×C₄×C₃₀₇
Frattini, cosocle	C₂²	C₂³×C₃₀₇
prime radical	C₂⁴×C₃₀₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₀₇ ◁ G

132 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	#34087611, #34087653, #34087654, …
maximal subgroup of	#323×C₃₀₇, #342×C₃₀₇, C₄×C₂²⋊C₄×C₃₀₇, …
maximal normal subgroup of	#323×C₃₀₇, #342×C₃₀₇, C₄×C₂²⋊C₄×C₃₀₇, …
maximal quotient of	C₂×#95×C₃₀₇, C₄×C₂²⋊C₄×C₃₀₇, #379×C₃₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 22);