Finite Group Databasebeta

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C₂⁴×C₄×C₈×C₂₇ #72192051

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3044058071040
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₄×C₈×C₂₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄×C₉	C₂⁶×C₃
socle, prime radical	C₂⁶×C₃	C₂×C₄×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

75016 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×C₄×C₁₆×C₂₇, C₂⁴×C₈²×C₂₇, C₂³×C₄²×C₈×C₂₇, …
maximal normal subgroup of	C₂⁴×C₄×C₁₆×C₂₇, C₂⁴×C₈²×C₂₇, C₂³×C₄²×C₈×C₂₇, …
maximal quotient of	C₂⁴×C₄×C₁₆×C₂₇, C₂⁴×C₈²×C₂₇, C₂³×C₄²×C₈×C₂₇, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.