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C₄×C₉×C₁₉₃ #20294261

order	6948
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃²×C₆₄ (order 2304) · Inn(G) = C₁ · Out(G) = C₂²×C₃²×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₉₄₈
abelian	C₄×C₉×C₁₉₃
multiplicative	(ℤ/6949)ˣ, (ℤ/13898)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₃	C₂×C₃×C₁₉₃
socle	C₂×C₃×C₁₉₃	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6948 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₃₈₉₆, Dic₆₉₄₈
maximal subgroup of	C₄×C₅×C₉×C₁₉₃, C₉×Dic₅×C₁₉₃, C₉×AGL(1,𝔽₅)×C₁₉₃, …
maximal normal subgroup of	C₄×C₅×C₉×C₁₉₃, C₈×C₉×C₁₉₃, C₂×C₄×C₉×C₁₉₃, …
maximal quotient of	C₄×C₅×C₉×C₁₉₃, C₉×Dic₅×C₁₉₃, C₉×AGL(1,𝔽₅)×C₁₉₃, …
automorphism group of	C₆₉₄₉
outer automorphism group of	C₆₉₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6948, 1);