C₂×#485×C₇₉ #23760710

order	10112
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁴

Aliases

C₂×#485×C₇₉

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

416 conjugacy classes of subgroups.

3002 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1820);