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C₂²×C₃²×C₄×C₉₇ #72192168

order	13968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 884736
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃

Aliases

abelian	C₂²×C₃²×C₄×C₉₇
multiplicative	(ℤ/24507)ˣ, (ℤ/49014)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₃²×C₉₇
socle, prime radical	C₂³×C₃²×C₉₇	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13968 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₃²×C₈×C₉₇, C₂×C₃²×C₄²×C₉₇, C₂³×C₃²×C₄×C₉₇
maximal normal subgroup of	C₂²×C₃²×C₈×C₉₇, C₂×C₃²×C₄²×C₉₇, C₂³×C₃²×C₄×C₉₇
maximal quotient of	C₂²×C₃²×C₈×C₉₇, C₂×C₃²×C₄²×C₉₇, C₂³×C₃²×C₄×C₉₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.