C₂²×Q₃₂×C₇₉ #23761032

order	10112
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂²×Q₃₂×C₇₉

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₉	D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₇₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₈×C₇₉ ◁ G

360 conjugacy classes of subgroups.

3476 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 2142);