Finite Group Databasebeta

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C5×#84074 #14411752

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#84074

Splittings

HallC3×C5 ⋊ #2879
SylowC3 ⋊ C5×#2879

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC22×C3×C5×#41C2
socleC22×C3×C5C23×C4
cosocleC2×C3×C4C24×C5
hypercenterC22×C5×#41D3
hypocenterC3C5×#2879
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×#41

1528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137450);