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C13×C3⋊#170 #13095613

order1560
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C8×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊#170
unambiguous semidirect productC3⋊(C13×#170)

Splittings

derived, HallC3×C5 ⋊ C8×C13
HallC3×C5×C13 ⋊ C8
HallC5×C13 ⋊ C3⋊C8
HallC3×C13 ⋊ #170
SylowC5 ⋊ C13×C3⋊C8
SylowC3 ⋊ C13×#170

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽16)
commutator, hypocenterC3×C5C8×C13
FrattiniC2C13×ΓL(1,𝔽16)
Fitting, socle, prime radicalC2×C3×C5×C13C4
cosocleC3×Dic5C2×C13
LCSG ▷ C3×C5
UCSC1 ◁ C2×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)(15,16,17,18)(20,21)(22,23,24,26,25,27,28,29);(14,15,18,16,17)(19,20,21)

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 49);