Finite Group Databasebeta

← Prev (#14304760) Next (#14304762) →

C5×#70371 #14304761

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#70371

Splittings

HallC3×C5 ⋊ #1937
SylowC3 ⋊ C5×#1937

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#104C2
socleC22×C3×C5C4×D4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#104D3
hypocenterC3C5×#1937
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#104

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 30459);