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C₂²×C₄×C₆₂₅ #72188676

order	10000
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 96000
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₆₂₅
multiplicative	(ℤ/25000)ˣ, (ℤ/37500)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₂₅	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂×C₁₂₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

135 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₈×C₆₂₅, C₂×C₄²×C₆₂₅, C₂³×C₄×C₆₂₅, …
maximal normal subgroup of	C₂²×C₈×C₆₂₅, C₂×C₄²×C₆₂₅, C₂³×C₄×C₆₂₅, …
maximal quotient of	C₂²×C₈×C₆₂₅, C₂×C₄²×C₆₂₅, C₂³×C₄×C₆₂₅, …
automorphism group of	C₈×C₃₁₂₅
outer automorphism group of	C₈×C₃₁₂₅

GAP

Past the SmallGroups library coverage — no SmallGroups id.