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C₂×C₃×C₄²×C₇×C₈ #72184690

order	5376
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 75497472
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄³

Aliases

abelian	C₂×C₃×C₄²×C₇×C₈
multiplicative	(ℤ/12064)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃×C₇
socle, prime radical	C₂⁴×C₃×C₇	C₂²×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

4092 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄²×C₇×C₁₆, C₂×C₃×C₄×C₇×C₈², C₃×C₄³×C₇×C₈, …
maximal normal subgroup of	C₂×C₃×C₄²×C₇×C₁₆, C₂×C₃×C₄×C₇×C₈², C₃×C₄³×C₇×C₈, …
maximal quotient of	C₂×C₃×C₄²×C₇×C₁₆, C₂×C₃×C₄×C₇×C₈², C₃×C₄³×C₇×C₈, …
automorphism group of	C₁₃×C₂₉×C₃₂
outer automorphism group of	C₁₃×C₂₉×C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.