C₃⋊D₃×C₈₃ #13093648

order	1494
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₈₃
unambiguous semidirect product	C₃⋊(D₃×C₈₃)

Splittings

Fitting, socle, Hall	C₃²×C₈₃ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₈₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₈₃
Frattini	C₁	G
Fitting, socle	C₃²×C₈₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₈₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 747

A minimal faithful permutation representation — 3 generators on 89 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃⋊D₃×D₈₃, D₃²×C₈₃, (C₃⋊D₃)⋊D₈₃, …
maximal normal subgroup of	C₃⋊D₃×D₈₃, D₃²×C₈₃, (C₃⋊D₃)⋊D₈₃, …
maximal quotient of	C₃⋊Dic₃×C₈₃, C₂×C₃⋊D₃×C₈₃, C₈₃×C₃⋊D₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1494, 8);

C3⋊D3×C83 #13093648