Finite Group Databasebeta

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C₂×C₃³×C₈×C₂₅ #72189342

order	10800
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3594240
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×C₃³×C₈×C₂₅

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₅	C₂²×C₃³×C₅
socle, prime radical	C₂²×C₃³×C₅	C₄×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

924 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×C₁₆×C₂₅, C₃³×C₄×C₈×C₂₅, C₂²×C₃³×C₈×C₂₅, …
maximal normal subgroup of	C₂×C₃³×C₁₆×C₂₅, C₃³×C₄×C₈×C₂₅, C₂²×C₃³×C₈×C₂₅, …
maximal quotient of	C₂×C₃³×C₁₆×C₂₅, C₃³×C₄×C₈×C₂₅, C₂²×C₃³×C₈×C₂₅, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.