Finite Group Databasebeta

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C₂⁴×C₄×C₈×C₉ #72184100

order	4608
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1014686023680
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₄×C₈×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃×C₄	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂×C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

56262 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4608 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₄×C₉×C₁₆, C₂⁴×C₈²×C₉, C₂³×C₄²×C₈×C₉, …
maximal normal subgroup of	C₂⁴×C₄×C₉×C₁₆, C₂⁴×C₈²×C₉, C₂³×C₄²×C₈×C₉, …
maximal quotient of	C₂⁴×C₄×C₉×C₁₆, C₂⁴×C₈²×C₉, C₂³×C₄²×C₈×C₉, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.