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C₄²×C₁₉² #72185019

order	5776
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 11819520
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄×C₁₉

Aliases

C₄²×C₁₉²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₁₉²
socle, prime radical	C₂²×C₁₉²	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

330 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₈×C₁₉², C₂×C₄²×C₁₉², C₃×C₄²×C₁₉², …
maximal normal subgroup of	C₄×C₈×C₁₉², C₂×C₄²×C₁₉², C₃×C₄²×C₁₉², …
maximal quotient of	C₄×C₈×C₁₉², C₂×C₄²×C₁₉², C₃×C₄²×C₁₉², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.