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C₄²×C₇×C₇₉ #72187693

order	8848
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 44928
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₇×C₇₉
multiplicative	(ℤ/9193)ˣ, (ℤ/11065)ˣ, (ℤ/18386)ˣ, (ℤ/22130)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₇×C₇₉
socle, prime radical	C₂²×C₇×C₇₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₃×C₄²×C₇×C₇₉
maximal normal subgroup of	C₄×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₃×C₄²×C₇×C₇₉
maximal quotient of	C₄×C₇×C₈×C₇₉, C₂×C₄²×C₇×C₇₉, C₃×C₄²×C₇×C₇₉
automorphism group of	C₂₉×C₃₁₇, C₅×C₂₂₁₃
outer automorphism group of	C₂₉×C₃₁₇, C₅×C₂₂₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.