Finite Group Databasebeta

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C5×#68928 #14298887

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

Aliases

direct productC5×#68928

Splittings

HallC3×C5 ⋊ #1837
SylowC3 ⋊ C5×#1837

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#341C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C2×Q8
cosocleC22×C3×C4C23×C5
hypercenterC5×#341D3
hypocenterC3C5×#1837
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C5×#341

376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24585);