Finite Group Databasebeta

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C₄²×C₅×C₇₉ #72185477

order	6320
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 29952
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₅×C₇₉
multiplicative	(ℤ/7925)ˣ, (ℤ/15850)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₅×C₇₉
socle, prime radical	C₂²×C₅×C₇₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₃×C₄²×C₅×C₇₉, …
maximal normal subgroup of	C₄×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₃×C₄²×C₅×C₇₉, …
maximal quotient of	C₄×C₅×C₈×C₇₉, C₂×C₄²×C₅×C₇₉, C₃×C₄²×C₅×C₇₉, …
automorphism group of	C₂₅×C₃₁₇
outer automorphism group of	C₂₅×C₃₁₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.