Finite Group Databasebeta

← Prev (#72192164) Next (#72192166) →

C₄²×C₉×C₉₇ #72192165

order	13968
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₉×C₉₇
multiplicative	(ℤ/14393)ˣ, (ℤ/28786)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂²×C₃×C₉₇
socle, prime radical	C₂²×C₃×C₉₇	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

90 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	C₄×C₈×C₉×C₉₇, C₂×C₄²×C₉×C₉₇
maximal normal subgroup of	C₄×C₈×C₉×C₉₇, C₂×C₄²×C₉×C₉₇
maximal quotient of	C₄×C₈×C₉×C₉₇, C₂×C₄²×C₉×C₉₇
automorphism group of	C₃₇×C₃₈₉
outer automorphism group of	C₃₇×C₃₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.