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C₂²×C₇×C₈×C₁₆ #72183236

order	3584
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 18874368
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₈

Aliases

abelian	C₂²×C₇×C₈×C₁₆
multiplicative	(ℤ/10848)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂⁴×C₇
socle, prime radical	C₂⁴×C₇	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

1924 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂²×C₇×C₈×C₃₂, C₂²×C₇×C₁₆², C₂³×C₇×C₈×C₁₆, …
maximal normal subgroup of	C₂²×C₇×C₈×C₃₂, C₂²×C₇×C₁₆², C₂³×C₇×C₈×C₁₆, …
maximal quotient of	C₂²×C₇×C₈×C₃₂, C₂²×C₇×C₁₆², C₂³×C₇×C₈×C₁₆, …
automorphism group of	C₃×C₃₂×C₁₁₃
outer automorphism group of	C₃×C₃₂×C₁₁₃

GAP

Past the SmallGroups library coverage — no SmallGroups id.