Finite Group Databasebeta

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C5×#79402 #14419568

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#79402

Splittings

FittingC3×C5×C8×D4 ⋊ C2
HallC3×C5 ⋊ #2968
SylowC3 ⋊ C5×#2968

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×C8×D4C2
socleC22×C3×C5C23×C4
prime radicalC5×#939C4
cosocleC2×C3×C4C24×C5
hypercenterC5×C8×D4D3
hypocenterC3C5×#2968
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×C8×D4

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 145266);