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C₂×M₁₆×#64408 #22626485

order	9344
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×M₁₆×#64408

Splittings

Fitting	C₂×M₁₆×C₇₃ ⋊ C₄
Sylow	C₇₃ ⋊ C₂×C₄×M₁₆

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂²×C₄²
Frattini	C₄	C₂³×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄²
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	H(3,ℤ/4)×#64408, #338×#64408, #339×#64408, …
maximal normal subgroup of	H(3,ℤ/4)×#64408, #338×#64408, #339×#64408, …
maximal quotient of	C₂×M₁₆×#10596833, M₁₆×#11924036, C₂×#22625129, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 21064);