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#442×C₇₉ #19098137

order	5056
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×D₄
commutator	C₄	C₂²×C₄×C₇₉
Frattini, cosocle	C₂×C₄	C₂³×C₇₉
prime radical	C₂×D₈×C₇₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄²×C₇₉ ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₉×AGL(1,ℤ/16), C₂×#442×C₇₉, C₇₉×#2943, …
maximal normal subgroup of	C₇₉×AGL(1,ℤ/16), C₂×#442×C₇₉, C₇₉×#2943, …
maximal quotient of	C₇₉×#1580, C₇₉×#1586, C₇₉×#1594, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5056, 123);