C₆₇×C₃⋊#1043 #34117287

order	20100
isoclinism	isoclinic class of C₃⋊#1043
automorphism	?
homology	Abelianization (H₁) = C₄×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×C₃⋊#1043
unambiguous semidirect product	C₃⋊(C₆₇×#1043)

Splittings

Fitting, socle, Hall	C₃×C₅²×C₆₇ ⋊ C₄
derived, Hall	C₃×C₅² ⋊ C₄×C₆₇
Hall	C₅²×C₆₇ ⋊ Dic₃
Hall	C₃×C₆₇ ⋊ #1043
Sylow	C₅² ⋊ Dic₃×C₆₇
Sylow	C₃ ⋊ C₆₇×#1043

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	C₃⋊#1043
commutator, hypocenter	C₃×C₅²	C₄×C₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₆₇	C₄
prime radical	C₃×C₅⋊D₅×C₆₇	C₂
cosocle	C₃×C₅⋊D₅	C₂×C₆₇
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₆₇

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 5025

A minimal faithful permutation representation — 3 generators on 80 points:

(2,3)(5,8,7,6)(10,13,12,11)(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);(1,2,3)(9,10,13,11,12);(4,5,8,6,7)

Conjugacy classes & character table

1608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 143);

C67×C3⋊#1043 #34117287