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C₂³×C₃×C₄×C₇² #72184173

order	4704
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 86704128
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₇

Aliases

abelian	C₂³×C₃×C₄×C₇²
multiplicative	(ℤ/9976)ˣ, (ℤ/11368)ˣ, (ℤ/14964)ˣ, (ℤ/17052)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂⁴×C₃×C₇²
socle, prime radical	C₂⁴×C₃×C₇²	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

2360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4704 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₃×C₇²×C₈, C₂²×C₃×C₄²×C₇², C₂⁴×C₃×C₄×C₇², …
maximal normal subgroup of	C₂³×C₃×C₇²×C₈, C₂²×C₃×C₄²×C₇², C₂⁴×C₃×C₄×C₇², …
maximal quotient of	C₂³×C₃×C₇²×C₈, C₂²×C₃×C₄²×C₇², C₂⁴×C₃×C₄×C₇², …
automorphism group of	C₈×C₂₉×C₄₃, C₈×C₂₉×C₄₉
outer automorphism group of	C₈×C₂₉×C₄₃, C₈×C₂₉×C₄₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.