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C₂²×C₄×C₆₅₃ #23782575

order	10448
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 125184
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³

Aliases

abelian	C₂²×C₄×C₆₅₃
multiplicative	(ℤ/19605)ˣ, (ℤ/20912)ˣ, (ℤ/26140)ˣ, (ℤ/39210)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂³×C₆₅₃
socle, prime radical	C₂³×C₆₅₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10448 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#35229634, C₂²⋊#19104916, C₂×C₄×Dic₆₅₃, …
maximal subgroup of	#95×C₆₅₃, C₂²⋊C₈×C₆₅₃, C₂×C₄²×C₆₅₃, …
maximal normal subgroup of	#95×C₆₅₃, C₂²⋊C₈×C₆₅₃, C₂×C₄²×C₆₅₃, …
maximal quotient of	C₂×C₄²×C₆₅₃, C₂×C₂²⋊C₄×C₆₅₃, C₂×C₄⋊C₄×C₆₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10448, 10);