C₅×C₁₃⋊D₂₄₇ #44545773

order	32110
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₅×C₁₃⋊D₂₄₇
unambiguous semidirect product	C₁₃⋊(C₅×D₂₄₇)
unambiguous semidirect product	C₁₉⋊(C₅×C₁₃⋊D₁₃)

Splittings

Fitting, socle, Hall	C₅×C₁₃²×C₁₉ ⋊ C₂
derived, Hall	C₁₃²×C₁₉ ⋊ C₂×C₅
Hall	C₅×C₁₃² ⋊ D₁₉
Sylow	C₁₃² ⋊ C₅×D₁₉
Hall	C₅×C₁₉ ⋊ C₁₃⋊D₁₃
Sylow	C₁₉ ⋊ C₅×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₁₃⋊D₂₄₇
commutator, cosocle, hypocenter	C₁₃²×C₁₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₃²×C₁₉	C₂
LCS	G ▷ C₁₃²×C₁₉
UCS	C₁ ◁ C₅

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 16055

A minimal faithful permutation representation — 3 generators on 50 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50);(19,20,22,24,26,28,30,31,29,27,25,23,21)(32,33,35,37,39,41,43,45,47,49,50,48,46,44,42,40,38,36,34);(6,7,9,11,13,15,17,18,16,14,12,10,8)

Conjugacy classes & character table

8035 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32110, 14);

C5×C13⋊D247 #44545773