Dic₃×C₂₃×C₇₃ #34117883

order	20148
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₃×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₂₃×C₇₃
unambiguous semidirect product	C₃⋊(C₄×C₂₃×C₇₃)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₂₃×C₇₃
Hall	C₃×C₂₃×C₇₃ ⋊ C₄
Hall	C₃×C₇₃ ⋊ C₄×C₂₃
Hall	C₃×C₂₃ ⋊ C₄×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₃×C₇₃	D₃
commutator, hypocenter	C₃	C₄×C₂₃×C₇₃
Frattini	C₂	D₃×C₂₃×C₇₃
Fitting, socle, prime radical	C₂×C₃×C₂₃×C₇₃	C₂
cosocle	C₂×C₃	C₂×C₂₃×C₇₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₂₃×C₇₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 20148

A minimal faithful permutation representation — 2 generators on 103 points:

(2,3)(4,7,6,5)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,2,3)

Conjugacy classes & character table

10074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20148, 6);

Dic3×C23×C73 #34117883