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C5×#68905 #14297765

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

Aliases

direct productC5×#68905

Splittings

HallC3×C5 ⋊ #1805
SylowC3 ⋊ C5×#1805

Subgroups

subgroupG/H
centerC23×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#340C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#340D3
hypocenterC3C5×#1805
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5 ◁ C5×#340

584 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)(17,19,20,26)(18,23,22,31)(21,30,28,27)(24,32,29,25);(7,8)(13,14,15,16)(18,22)(23,31)(24,29)(25,32);(9,10,11,12)(14,16)(17,18)(19,25)(20,22)(21,29)(23,27)(24,28)(26,32)(30,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23463);