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C5×#68084 #14286383

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC5×#68084

Splittings

HallC3×C5 ⋊ #1579
SylowC3 ⋊ C5×#1579

Subgroups

subgroupG/H
centerC2×C4×C5C2×D12
commutatorC3×C4C22×C5×C8
FrattiniC42C22×C5×D3
FittingC3×C5×#322C2
socle, prime radicalC22×C3×C5C4×D4
cosocleC3×C42C23×C5
hypercenterC5×#322D3
hypocenterC3C5×#1579
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C4×C5×C8 ◁ C5×#322

320 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)(9,11,12,16,13,10,14,15)(18,23)(22,31)(24,28)(25,32);(7,8)(17,19,21,27)(18,22,23,31)(20,29,30,26)(24,32,28,25);(7,8)(9,10,12,15,13,11,14,16)(17,18)(19,25)(20,28)(21,23)(22,26)(24,30)(27,32)(29,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 12081);