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C3×C13×#170 #13095607

order1560
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C8×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×#170

Splittings

derived, SylowC5 ⋊ C3×C8×C13
HallC3×C5×C13 ⋊ C8
HallC5×C13 ⋊ C3×C8
HallC3×C5 ⋊ C8×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13AGL(1,𝔽5)
commutator, hypocenterC5C3×C8×C13
FrattiniC2C3×C13×AGL(1,𝔽5)
Fitting, socle, prime radicalC2×C3×C5×C13C4
cosocleDic5C2×C3×C13
LCSG ▷ C5
UCSC1 ◁ C2×C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1560

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(18,19,20,21)(22,23,24,26,25,27,28,29);(17,18,19,21,20)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 43);