Finite Group Databasebeta

← Prev (#14281022) Next (#14281024) →

C5×#71572 #14281023

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

Aliases

direct productC5×#71572

Splittings

HallC3×C5 ⋊ #1464
SylowC3 ⋊ C5×#1464

Subgroups

subgroupG/H
centerC22×C5C2×#217
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#1464
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C2×C5×#117

504 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(10,13)(14,16)(17,20,21,28)(18,23,24,30)(19,26,27,32)(22,29,25,31);(17,19)(18,22)(20,26)(21,27)(23,29)(24,25)(28,32)(30,31);(7,8)(9,10,11,14,12,13,15,16)(17,18)(19,25,27,22)(20,23)(21,24)(26,31,32,29)(28,30)

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, 6721);