Finite Group Databasebeta

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C₂×C₃×C₄×C₇²×C₈ #72188175

order	9408
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8257536
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄×C₇

Aliases

C₂×C₃×C₄×C₇²×C₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂³×C₃×C₇²
socle, prime radical	C₂³×C₃×C₇²	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

1620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9408 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₇²×C₁₆, C₂×C₃×C₇²×C₈², C₃×C₄²×C₇²×C₈, …
maximal normal subgroup of	C₂×C₃×C₄×C₇²×C₁₆, C₂×C₃×C₇²×C₈², C₃×C₄²×C₇²×C₈, …
maximal quotient of	C₂×C₃×C₄×C₇²×C₁₆, C₂×C₃×C₇²×C₈², C₃×C₄²×C₇²×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.