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C₂×#16839518 #21445519

order	7808
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×#16839518

Splittings

C₆₁ ⋊ C₂×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄×Dic₆₁
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#117×C₆₁	C₂
socle	C₂²×C₆₁	#95
hypercenter	C₂×#117	D₆₁
hypocenter	C₆₁	C₂×H(3,ℤ/4)
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1244 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	H(3,ℤ/4)×Dic₆₁, C₄×#16839518, #29585181, …
maximal normal subgroup of	H(3,ℤ/4)×Dic₆₁, C₄×#16839518, #29585181, …
maximal quotient of	C₂×#21443647, C₂×#21443648, #29569411, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7808, 4210);