C₁₃×#3796 #14273252

order	1872
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃²×C₁₃ ⋊ #41
Sylow	C₃² ⋊ C₁₃×#41

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

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

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 312

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,16,17,20)(15,18,19,21)(22,23,24)(25,26,27);(14,15,17,19)(16,21,20,18)(23,24);(16,20)(18,21)(26,27)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1872, 880);