C₇₉×#2675 #23760297

order	10112
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₉ · Schur multiplier (H₂) = C₂⁶

Aliases

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

804 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 224 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, 1407);