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C₁₂₄₉₁ #27159692

order	12491
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₅×C₁₂₄₉ (order 12490) · Inn(G) = C₁ · Out(G) = C₂×C₅×C₁₂₄₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

C₁₂₄₉₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₁

2 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12491 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup of	D₁₂₄₉₁
Fitting subgroup of	D₁₂₄₉₁
socle of	D₁₂₄₉₁
maximal subgroup of	D₁₂₄₉₁, C₂×C₁₂₄₉₁, C₃×C₁₂₄₉₁
maximal normal subgroup of	D₁₂₄₉₁, C₂×C₁₂₄₉₁, C₃×C₁₂₄₉₁
maximal quotient of	C₂×C₁₂₄₉₁, C₃×C₁₂₄₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12491, 1);