Finite Group Databasebeta

← Prev (#14303132) Next (#14303134) →

C5×#69482 #14303133

order1920
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#69482

Splittings

HallC3×C5 ⋊ #1916
SylowC3 ⋊ C5×#1916

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC22×C3C22×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C5×#1916
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C4⋊C4

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28831);