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C5×C3⋊((C17⋊D17)⋊C3) #39907239

order26010
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C17

Aliases

direct productC5×C3⋊((C17⋊D17)⋊C3)
unambiguous semidirect productC3⋊(C5×(C17⋊D17)⋊C3)
unambiguous semidirect product(C3⋊(C17⋊D17))⋊(C3×C5)
unambiguous semidirect product(C5×C3⋊(C17⋊D17))⋊C3

Splittings

Fitting, socleC3×C5×C172 ⋊ C2×C3
derivedC3×C172 ⋊ C2×C3×C5
HallC3×C5×C172⋊C3 ⋊ C2
HallC3×C172⋊C3 ⋊ C2×C5
HallC5×C172 ⋊ C3×D3
SylowC172 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC5C3⋊((C17⋊D17)⋊C3)
commutator, cosocle, hypocenterC3×C172C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C172C2×C3
LCSG ▷ C3×C172
UCSC1 ◁ C5

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 59
transitive degreeμt(G) = 765

A minimal faithful permutation representation — 2 generators on 59 points:

(1,2,3,4,5)(6,7,9)(8,22,23,12,13,35)(10,32,34,17,18,27)(11,16,40,20,21,31)(14,24,15,25,26,28)(19,48,51,36,37,56)(29,54,39,47,45,33)(30,50,42,43,49,38)(41,55,44,46,53,52)(58,59);(6,8,14,27,45,55,56,31,50,49,40,51,53,54,34,25,12)(7,10,19,38,52,26,22,33,11,20,39,13,24,44,42,36,17)(9,15,29,48,43,21,41,18,35,23,32,46,16,30,37,47,28)(57,58,59)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26010, 53);