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C₂×#16863152 #22559909

order	8576
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

C₂×#16863152

Splittings

C₆₇ ⋊ C₂×H(3,ℤ/4)

Subgroups

	subgroup	G/H
center	C₂×C₄	C₄×Dic₆₇
commutator	C₄×C₆₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₇
Fitting	C₂×#117×C₆₇	C₂
socle	C₂²×C₆₇	#95
hypercenter	C₂×#117	D₆₇
hypocenter	C₆₇	C₂×H(3,ℤ/4)
LCS	G ▷ C₄×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	H(3,ℤ/4)×Dic₆₇, C₄×#16863152, #30760999, …
maximal normal subgroup of	H(3,ℤ/4)×Dic₆₇, C₄×#16863152, #30760999, …
maximal quotient of	C₂×#22558037, C₂×#22558038, #30745229, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8576, 4210);