#67×C₇₃ #13182136

order	1752
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇₃ · Schur multiplier (H₂) = C₂

supersolvable
metabelian
solvable
monomial

Aliases

direct product

#67×C₇₃

Splittings

Fitting	C₂²×C₃×C₇₃ ⋊ C₂
Hall	C₃×C₇₃ ⋊ D₄
Sylow	C₃ ⋊ D₄×C₇₃

Subgroups

	subgroup	G/H
center	C₂×C₇₃	C₂×D₃
commutator, cosocle	C₂×C₃	C₂²×C₇₃
Frattini	C₂	C₂×D₃×C₇₃
Fitting	C₂²×C₃×C₇₃	C₂
socle	C₂×C₃×C₇₃	C₂²
hypercenter	C₂²×C₇₃	D₃
hypocenter	C₃	D₄×C₇₃
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂²×C₇₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 876

A minimal faithful permutation representation — 2 generators on 80 points:

(1,2,3)(5,7)(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);(2,3)(4,5)(6,7)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1752, 36);

#67×C73 #13182136