C₁₁×D₇×C₃⋊D₂₁ #34085025

order	19404
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₁₁×D₇×C₃⋊D₂₁
unambiguous semidirect product	(C₃×D₇)⋊(C₁₁×D₂₁)
unambiguous semidirect product	(C₇×D₇)⋊(C₁₁×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₁₁	D₇×C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇²	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₁	C₂²
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₁

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

normal subgroups only

This group has 312 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) = 31
transitive degree	μ_t(G) = 1386

A minimal faithful permutation representation — 3 generators on 31 points:

(2,3)(5,6)(7,8,10,12,13,11,9)(15,16)(17,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31);(4,5,6)(8,9)(10,11)(12,13)(14,15,17,19,20,18,16);(1,2,3)

1815 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 516);