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C₂×C₄²×C₇×C₄₇ #72189133

order	10528
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 423936
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄²×C₇×C₄₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂³×C₇×C₄₇
socle, prime radical	C₂³×C₇×C₄₇	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₇×C₈×C₄₇, C₄³×C₇×C₄₇, C₂²×C₄²×C₇×C₄₇, …
maximal normal subgroup of	C₂×C₄×C₇×C₈×C₄₇, C₄³×C₇×C₄₇, C₂²×C₄²×C₇×C₄₇, …
maximal quotient of	C₂×C₄×C₇×C₈×C₄₇, C₄³×C₇×C₄₇, C₂²×C₄²×C₇×C₄₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.