C₃×C₁₉×C₇₃⋊C₃ #27159673

order	12483
isoclinism	isoclinic class of C₇₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₉×C₇₃⋊C₃
unambiguous semidirect product	C₇₃⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₃×C₇₃)⋊(C₃×C₁₉)

Splittings

Fitting, socle	C₃×C₁₉×C₇₃ ⋊ C₃
derived, Sylow	C₇₃ ⋊ C₃²×C₁₉
Hall	C₁₉×C₇₃ ⋊ C₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₇₃⋊C₃
commutator, cosocle, hypocenter	C₇₃	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₇₃	C₃
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 4161

A minimal faithful permutation representation — 2 generators on 95 points:

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

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₉×D₇₃⋊C₃, C₃×(C₇₃⋊C₃)⋊D₁₉, C₃×D₁₉×C₇₃⋊C₃, …
maximal normal subgroup of	C₃×C₁₉×D₇₃⋊C₃, C₃×(C₇₃⋊C₃)⋊D₁₉, C₃×D₁₉×C₇₃⋊C₃, …
maximal quotient of	C₂×C₃×C₁₉×C₇₃⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12483, 23);

C3×C19×C73⋊C3 #27159673