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C5×#69755 #14296180

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#69755

Splittings

HallC3×C5 ⋊ #1768
SylowC3 ⋊ C5×#1768

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC22×C3C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C5×#1768
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C2×C4×C5×C8

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21878);