C₅×D₃×C₇₃ #14555463

order	2190
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₇₃
unambiguous semidirect product	C₃⋊(C₂×C₅×C₇₃)

Splittings

Fitting, socle, Hall	C₃×C₅×C₇₃ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₅×C₇₃
Hall	C₃×C₇₃ ⋊ C₂×C₅
Hall	C₃×C₅ ⋊ C₂×C₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₇₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₇₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₇₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 1095

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2,3,4,5)(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);(7,8)

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₃×D₇₃, D₃×D₅×C₇₃, D₃×D₃₆₅, …
maximal normal subgroup of	C₅×D₃×D₇₃, D₃×D₅×C₇₃, D₃×D₃₆₅, …
maximal quotient of	C₅×Dic₃×C₇₃, C₂×C₅×D₃×C₇₃, D₃×C₂₅×C₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2190, 6);

C5×D3×C73 #14555463