C₃×D₇×C₇⋊AGL(1,𝔽₁₁) #44568587

order	32340
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×D₇×C₇⋊AGL(1,𝔽₁₁)
unambiguous semidirect product	(C₃×D₇×D₇₇)⋊C₅

	subgroup	G/H
center, hypercenter	C₃	D₇×C₇⋊AGL(1,𝔽₁₁)
commutator, cosocle, hypocenter	C₇²×C₁₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₁	C₂²×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₃

208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

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

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 462

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 289);