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C₇×C₁₆×C₇₉ #72187692

order	8848
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃²×C₄×C₁₃ (order 3744) · Inn(G) = C₁ · Out(G) = C₂³×C₃²×C₄×C₁₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₈₈₄₈
abelian	C₇×C₁₆×C₇₉
multiplicative	(ℤ/8849)ˣ, (ℤ/17698)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₇×C₇₉
socle, prime radical	C₂×C₇×C₇₉	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

derived subgroup of	Dic₈₈₄₈, D₁₇₆₉₆
maximal subgroup of	C₇×C₃₂×C₇₉, C₂×C₇×C₁₆×C₇₉, C₃×C₇×C₁₆×C₇₉, …
maximal normal subgroup of	C₇×C₃₂×C₇₉, C₂×C₇×C₁₆×C₇₉, C₃×C₇×C₁₆×C₇₉, …
maximal quotient of	C₇×C₃₂×C₇₉, C₂×C₇×C₁₆×C₇₉, C₃×C₇×C₁₆×C₇₉
automorphism group of	C₈₈₄₉
outer automorphism group of	C₈₈₄₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.