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C₃₂×C₁₉₃ #20259754

order	6176
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×C₈×C₆₄ (order 3072) · Inn(G) = C₁ · Out(G) = C₂×C₃×C₈×C₆₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₆₁₇₆
abelian	C₃₂×C₁₉₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₁₆	C₂×C₁₉₃
socle	C₂×C₁₉₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6176 conjugacy classes. The character table is too large to display.

Relationships

center of	M₁₂₈×C₁₉₃, #2258×C₁₉₃
maximal subgroup of	C₆₄×C₁₉₃, C₂×C₃₂×C₁₉₃, M₆₄×C₁₉₃, …
maximal normal subgroup of	C₆₄×C₁₉₃, C₂×C₃₂×C₁₉₃, M₆₄×C₁₉₃, …
maximal quotient of	C₆₄×C₁₉₃, C₂×C₃₂×C₁₉₃, C₃×C₃₂×C₁₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6176, 1);