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C3×D13×D85 #27210550

order13260
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D13×D85

Splittings

Fitting, socle, HallC3×C5×C13×C17 ⋊ C22
derived, HallC5×C13×C17 ⋊ C22×C3
HallC3×C13×C17 ⋊ C2×D5
HallC3×C5×C17 ⋊ C2×D13
HallC13×C17 ⋊ C2×C3×D5
HallC3×C5×C13 ⋊ C2×D17
HallC5×C17 ⋊ C2×C3×D13
HallC5×C13 ⋊ C2×C3×D17
HallC3×C17 ⋊ D5×D13
HallC3×C13 ⋊ C2×D85
SylowC17 ⋊ C3×D5×D13
HallC3×C5 ⋊ D13×D17
SylowC13 ⋊ C2×C3×D85
SylowC5 ⋊ C3×D13×D17

Subgroups

subgroupG/H
center, hypercenterC3D13×D85
commutator, cosocle, hypocenterC5×C13×C17C22×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C17C22
LCSG ▷ C5×C13×C17
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 38
transitive degreeμt(G) = 3315

A minimal faithful permutation representation — 2 generators on 38 points:

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

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13260, 100);