C₅×C₁₁⋊(C₁₇⋊D₁₇) #44541120

order	31790
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₇

Aliases

direct product	C₅×C₁₁⋊(C₁₇⋊D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅×D₁₈₇)

Splittings

Fitting, socle, Hall	C₅×C₁₁×C₁₇² ⋊ C₂
derived, Hall	C₁₁×C₁₇² ⋊ C₂×C₅
Hall	C₅×C₁₇² ⋊ D₁₁
Sylow	C₁₇² ⋊ C₅×D₁₁
Hall	C₅×C₁₁ ⋊ C₁₇⋊D₁₇
Sylow	C₁₁ ⋊ C₅×C₁₇⋊D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊(C₁₇⋊D₁₇)
commutator, cosocle, hypocenter	C₁₁×C₁₇²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇²	C₂
LCS	G ▷ C₁₁×C₁₇²
UCS	C₁ ◁ C₅

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 15895

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

Conjugacy classes & character table

7955 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31790, 24);

C5×C11⋊(C17⋊D17) #44541120