Finite Group Databasebeta

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C₂⁴×C₃×C₄×C₈₁ #72193602

order	15552
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 10032906240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

abelian	C₂⁴×C₃×C₄×C₈₁
multiplicative	(ℤ/45640)ˣ, (ℤ/50856)ˣ, (ℤ/54768)ˣ, (ℤ/58680)ˣ, (ℤ/68040)ˣ, (ℤ/68460)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

12258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15552 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃×C₈×C₈₁, C₂³×C₃×C₄²×C₈₁, C₂⁵×C₃×C₄×C₈₁
maximal normal subgroup of	C₂⁴×C₃×C₈×C₈₁, C₂³×C₃×C₄²×C₈₁, C₂⁵×C₃×C₄×C₈₁
maximal quotient of	C₂⁴×C₃×C₈×C₈₁, C₂³×C₃×C₄²×C₈₁, C₂⁵×C₃×C₄×C₈₁

GAP

Past the SmallGroups library coverage — no SmallGroups id.