Finite Group Databasebeta

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C₂⁶×C₇×C₁₉ #72187392

order	8512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2177140654080
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂⁶×C₇×C₁₉

Subgroups

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

11300 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8512 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁵×C₄×C₇×C₁₉, C₂⁷×C₇×C₁₉, C₂⁶×C₃×C₇×C₁₉
maximal normal subgroup of	C₂⁵×C₄×C₇×C₁₉, C₂⁷×C₇×C₁₉, C₂⁶×C₃×C₇×C₁₉
maximal quotient of	C₂⁵×C₄×C₇×C₁₉, C₂⁷×C₇×C₁₉, C₂⁶×C₃×C₇×C₁₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.