C₇₉×#3104 #23760726

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

Aliases

	subgroup	G/H
center	C₂×C₄×C₇₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₉
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂³×C₇₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

384 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, 1836);