C₁₃×D₅₀₅ #27190050

order	13130
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₅₀₅
unambiguous semidirect product	C₅⋊(C₁₃×D₁₀₁)
unambiguous semidirect product	C₁₀₁⋊(D₅×C₁₃)

Splittings

Fitting, socle, Hall	C₅×C₁₃×C₁₀₁ ⋊ C₂
derived, Hall	C₅×C₁₀₁ ⋊ C₂×C₁₃
Hall	C₁₃×C₁₀₁ ⋊ D₅
Sylow	C₁₀₁ ⋊ D₅×C₁₃
Hall	C₅×C₁₃ ⋊ D₁₀₁
Sylow	C₅ ⋊ C₁₃×D₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₅₀₅
commutator, cosocle, hypocenter	C₅×C₁₀₁	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₀₁	C₂
LCS	G ▷ C₅×C₁₀₁
UCS	C₁ ◁ C₁₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 6565

A minimal faithful permutation representation — 2 generators on 119 points:

(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)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(103,104)(105,106)(107,108,109,110,111,112,113,114,115,116,117,118,119);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,103,105,106,104)

Conjugacy classes & character table

3302 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×#14523087, C₁₃×#14523088, #39910990, …
maximal normal subgroup of	C₁₃×#14523087, C₁₃×#14523088, #39910990, …
maximal quotient of	C₁₃×Dic₅₀₅, C₂×C₁₃×D₅₀₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13130, 7);

C13×D505 #27190050