Finite Group Databasebeta

← Prev (#14299622) Next (#14299624) →

C5×#70102 #14299623

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#70102

Splittings

HallC3×C5 ⋊ #1857
SylowC3 ⋊ C5×#1857

Subgroups

subgroupG/H
centerC22×C5#882
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#101C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#101D3
hypocenterC3C5×#1857
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#101

544 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)(13,15,17,22)(14,19,20,28)(16,25,23,21)(18,26,24,27);(7,8)(9,11,12,10)(13,14)(15,19)(16,24)(17,20)(18,23)(21,26)(22,28)(25,27);(7,8)(9,10,12,11)(14,18)(16,23)(19,27)(20,24)(21,25)(26,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25321);