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C₈×C₁₃₉₉ #26014141

order	11192
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₂₃₃ (order 5592) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₂₃₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₁₉₂
abelian	C₈×C₁₃₉₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₁₃₉₉
socle, prime radical	C₂×C₁₃₉₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11192 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₁₃₉₉⋊C₁₆, C₈×D₁₃₉₉, #36375553, …
maximal subgroup of	C₁₆×C₁₃₉₉, C₂×C₈×C₁₃₉₉, M₁₆×C₁₃₉₉, …
maximal normal subgroup of	C₁₆×C₁₃₉₉, C₂×C₈×C₁₃₉₉, M₁₆×C₁₃₉₉, …
maximal quotient of	C₁₆×C₁₃₉₉, C₂×C₈×C₁₃₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11192, 1);