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C₂²×C₄×C₆₁₉ #23755233

order	9904
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 118656
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₆₁₉
multiplicative	(ℤ/19816)ˣ, (ℤ/29724)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₆₁₉
socle, prime radical	C₂³×C₆₁₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9904 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₆₁₉⋊#95, C₂²⋊(C₆₁₉⋊C₈), C₂×C₄×Dic₆₁₉, …
maximal subgroup of	#95×C₆₁₉, C₂²⋊C₈×C₆₁₉, C₂×C₄²×C₆₁₉, …
maximal normal subgroup of	#95×C₆₁₉, C₂²⋊C₈×C₆₁₉, C₂×C₄²×C₆₁₉, …
maximal quotient of	C₂×C₄²×C₆₁₉, C₂×C₂²⋊C₄×C₆₁₉, C₂×C₄⋊C₄×C₆₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9904, 10);