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C₂×C₆₁×#376 #21442308

order	7808
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₆₁ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

C₂×C₆₁×#376

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₆₁	C₂²
commutator	C₂	C₂²×C₄²×C₆₁
Frattini, cosocle	C₂³	C₂⁴×C₆₁
socle, prime radical	C₂⁴×C₆₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₁ ◁ G

840 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₂×#21443648, #29569415, #29569604, …
maximal subgroup of	C₂×C₆₁×#1274, C₆₁×#7855, C₆₁×#7906, …
maximal normal subgroup of	C₂×C₆₁×#1274, C₆₁×#7855, C₆₁×#7906, …
maximal quotient of	C₂×C₄×#95×C₆₁, C₄×C₆₁×#376, C₂×C₆₁×#1434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7808, 999);