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C5×D3553 #48001044

order35530
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3553
unambiguous semidirect productC17⋊(C5×D209)
unambiguous semidirect productC19⋊(C5×D187)

Splittings

Fitting, socle, HallC5×C11×C17×C19 ⋊ C2
derived, HallC11×C17×C19 ⋊ C2×C5
HallC5×C17×C19 ⋊ D11
HallC5×C11×C19 ⋊ D17
HallC5×C11×C17 ⋊ D19
HallC17×C19 ⋊ C5×D11
HallC11×C19 ⋊ C5×D17
HallC11×C17 ⋊ C5×D19
HallC5×C19 ⋊ D187
HallC5×C17 ⋊ D209
HallC5×C11 ⋊ D323
SylowC19 ⋊ C5×D187
SylowC17 ⋊ C5×D209
SylowC11 ⋊ C5×D323

Subgroups

subgroupG/H
center, hypercenterC5D3553
commutator, cosocle, hypocenterC11×C17×C19C2×C5
FrattiniC1G
Fitting, socleC5×C11×C17×C19C2
LCSG ▷ C11×C17×C19
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 17765

A minimal faithful permutation representation — 2 generators on 52 points:

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

Conjugacy classes & character table

8890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35530, 9);