C₇₉×#4294 #27214003

order	13509
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇₉×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₉×C₇₉
Hall	C₁₉×C₇₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇₉	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₉×C₇₉
Frattini	C₃	C₁₉⋊C₃×C₇₉
Fitting, socle, prime radical	C₃×C₁₉×C₇₉	C₃
cosocle	C₃×C₁₉	C₃×C₇₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₇₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 13509

A minimal faithful permutation representation — 2 generators on 107 points:

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

Conjugacy classes & character table

2133 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇₉×#4294, D₇₉×#4294, C₇₉×#4294⋊C₂, …
maximal normal subgroup of	C₂×C₇₉×#4294, D₇₉×#4294, C₇₉×#4294⋊C₂, …
maximal quotient of	C₂×C₇₉×#4294

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13509, 2);

C79×#4294 #27214003