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C₄²×C₇×C₉₇ #72189409

order	10864
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 55296
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄

Aliases

abelian	C₄²×C₇×C₉₇
multiplicative	(ℤ/11281)ˣ, (ℤ/22562)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₇×C₉₇
socle, prime radical	C₂²×C₇×C₉₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10864 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇×C₈×C₉₇, C₂×C₄²×C₇×C₉₇, C₃×C₄²×C₇×C₉₇
maximal normal subgroup of	C₄×C₇×C₈×C₉₇, C₂×C₄²×C₇×C₉₇, C₃×C₄²×C₇×C₉₇
maximal quotient of	C₄×C₇×C₈×C₉₇, C₂×C₄²×C₇×C₉₇, C₃×C₄²×C₇×C₉₇
automorphism group of	C₂₉×C₃₈₉
outer automorphism group of	C₂₉×C₃₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.