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C₂³×C₄×C₈×C₂₃ #19207676

order	5888
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1937768448
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

abelian	C₂³×C₄×C₈×C₂₃
multiplicative	(ℤ/22560)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₂×C₄	C₂⁵×C₂₃
socle	C₂⁵×C₂₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

4638 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₄×C₁₆×C₂₃, C₂³×C₈²×C₂₃, C₂²×C₄²×C₈×C₂₃, …
maximal normal subgroup of	C₂³×C₄×C₁₆×C₂₃, C₂³×C₈²×C₂₃, C₂²×C₄²×C₈×C₂₃, …
maximal quotient of	C₂³×C₄×C₁₆×C₂₃, C₂³×C₈²×C₂₃, C₂²×C₄²×C₈×C₂₃, …
automorphism group of	C₃×C₅×C₃₂×C₄₇
outer automorphism group of	C₃×C₅×C₃₂×C₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 53038);