Finite Group Databasebeta

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C5×#67807 #14278851

order1920
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#67807

Splittings

HallC3×C5 ⋊ #1382
SylowC3 ⋊ C5×#1382

Subgroups

subgroupG/H
centerC2×C4×C5D24
commutatorC3×C8C42×C5
FrattiniC22×C8C2×C5×D3
FittingC22×C3×C5×C16C2
socleC22×C3×C5#102
prime radicalC23×C3×C5SD16
cosocleC22×C3×C8C22×C5
hypercenterC22×C5×C16D3
hypocenterC3C5×#1382
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C22×C5×C16

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5)(6,7,8)(13,15,17,26,30,41,31,42,19,28,16,25,18,27,33,43)(14,20,21,24,34,38,32,44,23,36,37,40,22,35,29,39);(7,8)(9,10,11,12)(13,14)(15,24)(16,29)(17,32)(18,34)(19,23)(20,25)(21,31)(22,30)(26,36)(27,44)(28,40)(33,37)(35,43)(38,42)(39,41)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4549);