Finite Group Databasebeta

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C₂⁵×C₃×C₄²×C₉ #72192064

order	13824
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 108709401832980480
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²⁰×C₃×C₄

Aliases

C₂⁵×C₃×C₄²×C₉

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²×C₃	C₂⁷×C₃²
socle, prime radical	C₂⁷×C₃²	C₂²×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

1298580 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	C₂⁵×C₃×C₄×C₈×C₉, C₂⁴×C₃×C₄³×C₉, C₂⁶×C₃×C₄²×C₉
maximal normal subgroup of	C₂⁵×C₃×C₄×C₈×C₉, C₂⁴×C₃×C₄³×C₉, C₂⁶×C₃×C₄²×C₉
maximal quotient of	C₂⁵×C₃×C₄×C₈×C₉, C₂⁴×C₃×C₄³×C₉, C₂⁶×C₃×C₄²×C₉

GAP

Past the SmallGroups library coverage — no SmallGroups id.