Finite Group Databasebeta

← Prev (#72188645) Next (#72188647) →

C₂⁴×C₃×C₁₃×C₁₆ #72188646

order	9984
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 990904320
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

abelian	C₂⁴×C₃×C₁₃×C₁₆
multiplicative	(ℤ/32232)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂⁵×C₃×C₁₃
socle, prime radical	C₂⁵×C₃×C₁₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

5180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₁₃×C₃₂, C₂³×C₃×C₄×C₁₃×C₁₆, C₂⁵×C₃×C₁₃×C₁₆, …
maximal normal subgroup of	C₂⁴×C₃×C₁₃×C₃₂, C₂³×C₃×C₄×C₁₃×C₁₆, C₂⁵×C₃×C₁₃×C₁₆, …
maximal quotient of	C₂⁴×C₃×C₁₃×C₃₂, C₂³×C₃×C₄×C₁₃×C₁₆, C₂⁵×C₃×C₁₃×C₁₆, …
automorphism group of	C₃×C₈×C₁₇×C₇₉
outer automorphism group of	C₃×C₈×C₁₇×C₇₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.