Finite Group Databasebeta

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C5×#76309 #14330710

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

Aliases

direct productC5×#76309

Splittings

HallC3×C5 ⋊ #2376
SylowC3 ⋊ C5×#2376

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C3C24×C5
hypercenterC5×#390D3
hypocenterC3C5×#2376
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#390

1024 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)(14,18)(17,20)(22,25)(26,28);(7,8)(14,18)(15,19)(21,23,24,27)(22,26,25,28);(13,15)(14,17)(16,19)(18,20)(21,22)(23,26)(24,25)(27,28);(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)(22,25)(23,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 56408);