Finite Group Databasebeta

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C₂⁴×C₃³×C₄×C₈ #72192053

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1899492236328960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₃³×C₄

Aliases

C₂⁴×C₃³×C₄×C₈

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁶×C₃³
socle, prime radical	C₂⁶×C₃³	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

525112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₃³×C₄×C₁₆, C₂⁴×C₃³×C₈², C₂³×C₃³×C₄²×C₈, …
maximal normal subgroup of	C₂⁴×C₃³×C₄×C₁₆, C₂⁴×C₃³×C₈², C₂³×C₃³×C₄²×C₈, …
maximal quotient of	C₂⁴×C₃³×C₄×C₁₆, C₂⁴×C₃³×C₈², C₂³×C₃³×C₄²×C₈, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.