Finite Group Databasebeta

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C₂×C₃×C₄×C₇×C₈² #72189307

order	10752
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 603979776
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₄²×C₈

Aliases

C₂×C₃×C₄×C₇×C₈²

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄²	C₂⁴×C₃×C₇
socle, prime radical	C₂⁴×C₃×C₇	C₂×C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

7688 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10752 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃×C₄×C₇×C₈×C₁₆, C₂×C₃×C₇×C₈³, C₃×C₄²×C₇×C₈², …
maximal normal subgroup of	C₂×C₃×C₄×C₇×C₈×C₁₆, C₂×C₃×C₇×C₈³, C₃×C₄²×C₇×C₈², …
maximal quotient of	C₂×C₃×C₄×C₇×C₈×C₁₆, C₂×C₃×C₇×C₈³, C₃×C₄²×C₇×C₈², …

GAP

Past the SmallGroups library coverage — no SmallGroups id.