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C₂×#16810379 #20274415

order	6784
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×#16810379

Splittings

C₅₃ ⋊ C₂×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄×Dic₅₃
commutator	C₄×C₅₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₂×#117×C₅₃	C₂
socle	C₂²×C₅₃	#95
hypercenter	C₂×#117	D₅₃
hypocenter	C₅₃	C₂×H(3,ℤ/4)
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1084 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	H(3,ℤ/4)×Dic₅₃, C₄×#16810379, #27289260, …
maximal normal subgroup of	H(3,ℤ/4)×Dic₅₃, C₄×#16810379, #27289260, …
maximal quotient of	C₂×#20272543, C₂×#20272544, #27273490, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6784, 4210);