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C5×#71688 #14283156

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#71688

Splittings

HallC3×C5 ⋊ #1508
SylowC3 ⋊ C5×#1508

Subgroups

subgroupG/H
centerC22×C5C2×#217
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×C22⋊Q8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×C22⋊Q8D3
hypocenterC3C5×#1508
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C2×C5×C22⋊Q8

588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8854);