D₃×C₁₃×C₃⋊(C₇⋊D₇) #37525619

order	22932
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	D₃×C₁₃×C₃⋊(C₇⋊D₇)
unambiguous semidirect product	(C₃×D₃)⋊(C₁₃×C₇⋊D₇)
unambiguous semidirect product	(D₃×C₇)⋊(C₁₃×D₂₁)

	subgroup	G/H
center, hypercenter	C₁₃	D₃×C₃⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₃²×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₃

440 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.

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

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 3822

A minimal faithful permutation representation — 3 generators on 33 points:

(2,3)(4,5)(6,7)(9,10)(11,12)(13,14)(15,16,17)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33);(8,9,11,13,14,12,10)(16,17)(18,19,20);(1,2,4,6,7,5,3)

2925 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1564);