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C5×#68732 #14307437

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#68732

Splittings

HallC3×C5 ⋊ #1995
SylowC3 ⋊ C5×#1995

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#339D3
hypocenterC3C5×#1995
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 32 points:

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

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, 33135);