Finite Group Databasebeta

← Prev (#14301575) Next (#14301577) →

C5×#71724 #14301576

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71724

Splittings

HallC3×C5 ⋊ #1888
SylowC3 ⋊ C5×#1888

Subgroups

subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#124C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#124D3
hypocenterC3C5×#1888
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#124

688 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)(6,7,8)(13,16,18,25)(14,20,15,23)(17,26,19,24)(21,28,22,27);(7,8)(9,11,12,10)(13,15,18,14)(16,23,25,20)(17,21,19,22)(24,27,26,28);(7,8)(9,10,12,11)(13,14,19,22,18,15,17,21)(16,20,26,28,25,23,24,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27274);