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C₂⁵×C₃²×C₄×C₈ #72188017

order	9216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 64420386271395840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²⁰×C₃×C₄

Aliases

C₂⁵×C₃²×C₄×C₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁷×C₃²
socle, prime radical	C₂⁷×C₃²	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1224702 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9216 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₃²×C₄×C₁₆, C₂⁵×C₃²×C₈², C₂⁴×C₃²×C₄²×C₈, …
maximal normal subgroup of	C₂⁵×C₃²×C₄×C₁₆, C₂⁵×C₃²×C₈², C₂⁴×C₃²×C₄²×C₈, …
maximal quotient of	C₂⁵×C₃²×C₄×C₁₆, C₂⁵×C₃²×C₈², C₂⁴×C₃²×C₄²×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.