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D₈×C₉⋊D₉ #72244128

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

Aliases

D₈×C₉⋊D₉

Splittings

Fitting	C₉²×D₈ ⋊ C₂
Sylow	C₉² ⋊ C₂×D₈

Subgroups

	subgroup	G/H
center	C₂	D₄×C₉⋊D₉
commutator, cosocle	C₄×C₉²	C₂³
Frattini	C₃²×C₄	C₂²×C₃⋊D₃
Fitting	C₉²×D₈	C₂
socle	C₂×C₃²	D₄×C₃⋊D₃
hypercenter	D₈	C₉⋊D₉
hypocenter	C₉²	C₂×D₈
LCS	G ▷ C₄×C₉² ▷ C₂×C₉² ▷ C₉²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

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

normal subgroups only

This group has 874 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	C₂×D₈×C₉⋊D₉, AGL(1,ℤ/8)×C₉⋊D₉, D₈×#92314
maximal normal subgroup of	C₂×D₈×C₉⋊D₉, AGL(1,ℤ/8)×C₉⋊D₉, D₈×#92314
maximal quotient of	C₂×D₈×C₉⋊D₉, #102×C₉⋊D₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.