C₇₉×#3025 #23760647

order	10112
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center	C₄×C₇₉	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₇₉
socle	C₂×C₇₉	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ G

766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

2528 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1757);