Finite Group Databasebeta

← Prev (#72244105) Next (#72244107) →

SD₁₆×C₉⋊D₉ #72244106

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²×C₉

Aliases

SD₁₆×C₉⋊D₉

Splittings

Fitting	C₉²×SD₁₆ ⋊ C₂
Sylow	C₉² ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×C₉⋊D₉
commutator, cosocle	C₄×C₉²	C₂³
Frattini	C₃²×C₄	C₂²×C₃⋊D₃
Fitting	C₉²×SD₁₆	C₂
socle	C₂×C₃²	D₄×C₃⋊D₃
prime radical	D₄×C₉⋊D₉	C₂
hypercenter	SD₁₆	C₉⋊D₉
hypocenter	C₉²	C₂×SD₁₆
LCS	G ▷ C₄×C₉² ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

782 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 648

Conjugacy classes & character table

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

Relationships

maximal subgroup of	AGL(1,ℤ/8)×C₉⋊D₉, C₂×SD₁₆×C₉⋊D₉, SD₁₆×#92314
maximal normal subgroup of	AGL(1,ℤ/8)×C₉⋊D₉, C₂×SD₁₆×C₉⋊D₉, SD₁₆×#92314
maximal quotient of	#106×C₉⋊D₉, C₂×SD₁₆×C₉⋊D₉, #102×C₉⋊D₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.