C₆₇×C₄₃⋊C₇ #34117995

order	20167
isoclinism	isoclinic class of C₄₃⋊C₇
automorphism	?
homology	Abelianization (H₁) = C₇×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×C₄₃⋊C₇
unambiguous semidirect product	C₄₃⋊(C₇×C₆₇)
unambiguous semidirect product	(C₄₃×C₆₇)⋊C₇

Splittings

Fitting, socle, Hall	C₄₃×C₆₇ ⋊ C₇
derived, Sylow	C₄₃ ⋊ C₇×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₆₇	C₄₃⋊C₇
commutator, cosocle, hypocenter	C₄₃	C₇×C₆₇
Frattini	C₁	G
Fitting, socle	C₄₃×C₆₇	C₇
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₆₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 110
transitive degree	μ_t(G) = 2881

A minimal faithful permutation representation — 2 generators on 110 points:

(2,3,5,9,14,22,35)(4,7,11,18,29,40,6)(8,13,20,33,10,16,25)(12,17,27,38,21,32,43)(15,24,37,34,23,19,31)(26,36,28,39,30,41,42)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110);(1,2,4,8,5,10,17,28,11,19,32,22,20,34,24,37,14,23,36,33,25,35,40,43,38,31,42,18,30,39,41,27,29,16,26,9,15,13,21,7,12,3,6)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20167, 1);

C67×C43⋊C7 #34117995