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C₂²×C₃×C₄×C₉₇ #72184146

order	4656
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 36864
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₃×C₄×C₉₇
multiplicative	(ℤ/8169)ˣ, (ℤ/10892)ˣ, (ℤ/14004)ˣ, (ℤ/16338)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃×C₉₇
socle, prime radical	C₂³×C₃×C₉₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4656 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃×C₈×C₉₇, C₂×C₃×C₄²×C₉₇, C₂³×C₃×C₄×C₉₇, …
maximal normal subgroup of	C₂²×C₃×C₈×C₉₇, C₂×C₃×C₄²×C₉₇, C₂³×C₃×C₄×C₉₇, …
maximal quotient of	C₂²×C₃×C₈×C₉₇, C₂×C₃×C₄²×C₉₇, C₂³×C₃×C₄×C₉₇, …
automorphism group of	C₃×C₇×C₃₈₉, C₄×C₇×C₃₈₉
outer automorphism group of	C₃×C₇×C₃₈₉, C₄×C₇×C₃₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.