C₅×D₁₁×C₃⋊D₂₁ #28357693

order	13860
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₅×D₁₁×C₃⋊D₂₁

	subgroup	G/H
center, hypercenter	C₅	D₁₁×C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇×C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₁	C₂²
LCS	G ▷ C₃²×C₇×C₁₁
UCS	C₁ ◁ C₅

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 3465

A minimal faithful permutation representation — 3 generators on 29 points:

(2,3)(4,5)(6,7)(8,9,11,13,15,17,18,16,14,12,10)(20,21)(23,24)(25,26,27,28,29);(1,2,4,6,7,5,3)(9,10)(11,12)(13,14)(15,16)(17,18)(22,23,24);(19,20,21)

1155 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 360);