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C₂³×C₁₉×C₂₃ #72183157

order	3496
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 66528
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₁₉×C₂₃

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₄×C₁₉×C₂₃, C₂⁴×C₁₉×C₂₃, C₂³×C₃×C₁₉×C₂₃, …
maximal normal subgroup of	C₂²×C₄×C₁₉×C₂₃, C₂⁴×C₁₉×C₂₃, C₂³×C₃×C₁₉×C₂₃, …
maximal quotient of	C₂²×C₄×C₁₉×C₂₃, C₂⁴×C₁₉×C₂₃, C₂³×C₃×C₁₉×C₂₃, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.