Finite Group Databasebeta

← Prev (#72192011) Next (#72192013) →

C₂²×C₄×C₂₇×C₃₂ #72192012

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 14155776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

abelian	C₂²×C₄×C₂₇×C₃₂
multiplicative	(ℤ/41856)ˣ, (ℤ/51840)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₉×C₁₆	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂×C₉×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

2568 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₂₇×C₆₄, C₂²×C₈×C₂₇×C₃₂, C₂×C₄²×C₂₇×C₃₂, …
maximal normal subgroup of	C₂²×C₄×C₂₇×C₆₄, C₂²×C₈×C₂₇×C₃₂, C₂×C₄²×C₂₇×C₃₂, …
maximal quotient of	C₂²×C₄×C₂₇×C₆₄, C₂²×C₈×C₂₇×C₃₂, C₂×C₄²×C₂₇×C₃₂, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.