Finite Group Databasebeta

← Prev (#14545337) Next (#14545339) →

C₂×M₁₆×#595 #14545338

order	2176
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×M₁₆×#595

Splittings

Fitting	C₂×M₁₆×C₁₇ ⋊ C₄
Sylow	C₁₇ ⋊ C₂×C₄×M₁₆

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²×#595
commutator	C₂×C₁₇	C₂²×C₄²
Frattini	C₄	C₂³×#595
Fitting	C₂×M₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄²
prime radical	C₂³×D₁₇	C₂×C₄
cosocle	C₄×D₁₇	C₂⁴
hypercenter	C₂×M₁₆	#595
hypocenter	C₁₇	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 272

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	H(3,ℤ/4)×#595, #338×#595, #339×#595, …
maximal normal subgroup of	H(3,ℤ/4)×#595, #338×#595, #339×#595, …
maximal quotient of	C₂×M₁₆×#3624, M₁₆×#63242, C₂×#14543982, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 21064);