C₁₁×(C₂×D₃)⋊Dic₃ #13097066

order	1584
isoclinism	isoclinic class of #625
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₁₁×(C₂×D₃)⋊Dic₃
unambiguous semidirect product	(C₂×D₃)⋊(C₁₁×Dic₃)

Hall	C₃²×C₁₁ ⋊ C₂²⋊C₄
Sylow	C₃² ⋊ C₁₁×C₂²⋊C₄

152 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 528

A minimal faithful permutation representation — 2 generators on 25 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 230);