Finite Group Databasebeta

← Prev (#72194332) Next (#72194334) →

C₂²×C₄×C₈×C₁₂₈ #72194333

order	16384
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 206158430208
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁷×C₄²×C₈

Aliases

C₂²×C₄×C₈×C₁₂₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₆₄	C₂⁵
socle, prime radical	C₂⁵	C₂×C₄×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂×C₄×C₆₄ ▷ C₂×C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

36609 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₈×C₂₅₆, C₂²×C₄×C₁₆×C₁₂₈, C₂²×C₈²×C₁₂₈, …
maximal normal subgroup of	C₂²×C₄×C₈×C₂₅₆, C₂²×C₄×C₁₆×C₁₂₈, C₂²×C₈²×C₁₂₈, …
maximal quotient of	C₂²×C₄×C₈×C₂₅₆, C₂²×C₄×C₁₆×C₁₂₈, C₂²×C₈²×C₁₂₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.