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C5×#3516⋊C3 #14511354

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#3516⋊C3
unambiguous semidirect product#3516⋊(C3×C5)
unambiguous semidirect product(C5×#3516)⋊C3

Splittings

Fitting, HallC5×#3516 ⋊ C3
Sylow#3516 ⋊ C3×C5

Subgroups

subgroupG/H
center, socleC22×C5C23×A4
commutator, cosocleC2×Q8C23×C3×C5
FrattiniC22C23×C5×A4
FittingC5×#3516C3
hypercenterC5×#123A4
hypocenterQ8C3×C5×#41
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C5 ◁ C5×#123

534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 320

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237052);