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C₂³×C₈×C₁₁² #72186665

order	7744
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 567705600
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶×C₁₁

Aliases

abelian	C₂³×C₈×C₁₁²
multiplicative	(ℤ/16376)ˣ, (ℤ/24564)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₁₁²
socle, prime radical	C₂⁴×C₁₁²	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

2366 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7744 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₁₁²×C₁₆, C₂²×C₄×C₈×C₁₁², C₂⁴×C₈×C₁₁², …
maximal normal subgroup of	C₂³×C₁₁²×C₁₆, C₂²×C₄×C₈×C₁₁², C₂⁴×C₈×C₁₁², …
maximal quotient of	C₂³×C₁₁²×C₁₆, C₂²×C₄×C₈×C₁₁², C₂⁴×C₈×C₁₁², …
automorphism group of	C₈×C₂₃×C₈₉
outer automorphism group of	C₈×C₂₃×C₈₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.