Finite Group Databasebeta

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C5×#74053 #14322469

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25×C4

Aliases

direct productC5×#74053

Splittings

HallC3×C5 ⋊ #2310
SylowC3 ⋊ C5×#2310

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#381C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C3C24×C5
hypercenterC5×#381D3
hypocenterC3C5×#2310
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#381

1568 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)(6,7,8)(18,24)(22,25)(23,32)(30,31);(14,16)(17,20,21,29)(18,23,24,32)(19,26,27,28)(22,30,25,31);(7,8)(17,19,21,27)(18,22,24,25)(20,28,29,26)(23,31,32,30);(9,10,11,12)(13,14)(15,16)(17,18)(19,25)(20,23)(21,24)(22,27)(26,31)(28,30)(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, 48167);