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C₂⁴×C₄×C₉² #72184560

order	5184
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 40131624960
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰×C₉

Aliases

abelian	C₂⁴×C₄×C₉²
multiplicative	(ℤ/16872)ˣ, (ℤ/20520)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃²	C₂⁵×C₃²
socle, prime radical	C₂⁵×C₃²	C₂×C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

15663 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂⁴×C₈×C₉², C₂³×C₄²×C₉², C₂⁵×C₄×C₉², …
maximal normal subgroup of	C₂⁴×C₈×C₉², C₂³×C₄²×C₉², C₂⁵×C₄×C₉², …
maximal quotient of	C₂⁴×C₈×C₉², C₂³×C₄²×C₉², C₂⁵×C₄×C₉², …
automorphism group of	C₃×C₈×C₁₉×C₃₇, C₅×C₈×C₁₉×C₂₇
outer automorphism group of	C₃×C₈×C₁₉×C₃₇, C₅×C₈×C₁₉×C₂₇

GAP

Past the SmallGroups library coverage — no SmallGroups id.