Finite Group Databasebeta

← Prev (#72185308) Next (#72185310) →

C₂×C₃×C₄²×C₆₄ #72185309

order	6144
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 100663296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₃×C₄²×C₆₄
multiplicative	(ℤ/15440)ˣ, (ℤ/16640)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃₂	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂²×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

4368 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄²×C₁₂₈, C₂×C₃×C₄×C₈×C₆₄, C₃×C₄³×C₆₄, …
maximal normal subgroup of	C₂×C₃×C₄²×C₁₂₈, C₂×C₃×C₄×C₈×C₆₄, C₃×C₄³×C₆₄, …
maximal quotient of	C₂×C₃×C₄²×C₁₂₈, C₂×C₃×C₄×C₈×C₆₄, C₃×C₄³×C₆₄, …
automorphism group of	C₅×C₁₆×C₁₉₃, C₅×C₁₃×C₂₅₆
outer automorphism group of	C₅×C₁₆×C₁₉₃, C₅×C₁₃×C₂₅₆

GAP

Past the SmallGroups library coverage — no SmallGroups id.