Finite Group Databasebeta

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C5×#70773 #14284702

order1920
isoclinismisoclinic class of #4451
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#70773

Splittings

FittingC3×C5×#431 ⋊ C2
HallC3×C5 ⋊ #1543
SylowC3 ⋊ C5×#1543

Subgroups

subgroupG/H
centerC2×C4×C5(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#431C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5477C2
cosocleC3×C42C23×C5
hypercenterC5×#431D3
hypocenterC3C5×#1543
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#431

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 10400);