Finite Group Databasebeta

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C5×#82338 #14327999

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

Aliases

direct productC5×#82338

Splittings

HallC3×C5 ⋊ #2357
SylowC3 ⋊ C5×#2357

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C3C24×C5
hypercenterC2×C4×C5×D4D3
hypocenterC3C5×#2357
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4

1120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

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

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, 53697);