C₇₉×#2502 #23760124

order	10112
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

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

544 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 1234);