C₅×C₉⋊(C₁₇⋊D₁₇) #39907221

order	26010
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₇

Aliases

direct product	C₅×C₉⋊(C₁₇⋊D₁₇)
unambiguous semidirect product	C₉⋊(C₅×C₁₇⋊D₁₇)
unambiguous semidirect product	C₁₇⋊(C₅×D₁₅₃)

Splittings

Fitting, Hall	C₅×C₉×C₁₇² ⋊ C₂
derived, Hall	C₉×C₁₇² ⋊ C₂×C₅
Hall	C₅×C₁₇² ⋊ D₉
Sylow	C₁₇² ⋊ C₅×D₉
Hall	C₅×C₉ ⋊ C₁₇⋊D₁₇
Sylow	C₉ ⋊ C₅×C₁₇⋊D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₉⋊(C₁₇⋊D₁₇)
commutator, cosocle, hypocenter	C₉×C₁₇²	C₂×C₅
Frattini	C₃	C₅×C₃⋊(C₁₇⋊D₁₇)
Fitting	C₅×C₉×C₁₇²	C₂
socle	C₃×C₅×C₁₇²	D₃
LCS	G ▷ C₉×C₁₇²
UCS	C₁ ◁ C₅

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 13005

A minimal faithful permutation representation — 3 generators on 48 points:

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

Conjugacy classes & character table

6510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26010, 35);

C5×C9⋊(C17⋊D17) #39907221