C₃⋊C₈×C₇₃ #13182103

order	1752
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₈×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃⋊C₈×C₇₃
unambiguous semidirect product	C₃⋊(C₈×C₇₃)

Splittings

derived, Sylow	C₃ ⋊ C₈×C₇₃
Hall	C₃×C₇₃ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₇₃	D₃
commutator, hypocenter	C₃	C₈×C₇₃
Frattini	C₄	D₃×C₇₃
Fitting	C₃×C₄×C₇₃	C₂
socle, prime radical	C₂×C₃×C₇₃	C₄
cosocle	C₃×C₄	C₂×C₇₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₄×C₇₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 1752

A minimal faithful permutation representation — 2 generators on 84 points:

(2,3)(4,5,6,8,7,9,10,11)(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);(1,2,3)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1752, 3);

C3⋊C8×C73 #13182103