Finite Group Databasebeta

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C₄×(C₂×#3633)⋊C₄ #17981792

order	4352
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product	C₄×(C₂×#3633)⋊C₄
unambiguous semidirect product	#595⋊#336
unambiguous semidirect product	(C₂×#3633)⋊C₄²

Splittings

Fitting	C₂×C₄²×C₁₇ ⋊ C₈
Sylow	C₁₇ ⋊ C₄×#336

Subgroups

	subgroup	G/H
center	C₂²×C₄	C₂×#3633
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂³	C₂²×#3633
Fitting	C₂×C₄²×C₁₇	C₈
socle	C₂³×C₁₇	C₂²×C₈
prime radical	C₂³×D₁₇	C₂²×C₄
cosocle	C₂³×#595	C₂³
hypercenter	C₂×C₄²	#3633
hypocenter	C₁₇	C₄×#336
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1117036);