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C₂×C₃³×C₅²×C₈ #72189343

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 86261760
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³×C₅

Aliases

C₂×C₃³×C₅²×C₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃³×C₅²
socle, prime radical	C₂²×C₃³×C₅²	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

2464 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃³×C₅²×C₁₆, C₃³×C₄×C₅²×C₈, C₂²×C₃³×C₅²×C₈, …
maximal normal subgroup of	C₂×C₃³×C₅²×C₁₆, C₃³×C₄×C₅²×C₈, C₂²×C₃³×C₅²×C₈, …
maximal quotient of	C₂×C₃³×C₅²×C₁₆, C₃³×C₄×C₅²×C₈, C₂²×C₃³×C₅²×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.