Finite Group Databasebeta

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C5×#67808 #14278835

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

Aliases

direct productC5×#67808

Splittings

HallC3×C5 ⋊ #1381
SylowC3 ⋊ C5×#1381

Subgroups

subgroupG/H
centerC2×C4×C5D24
commutatorC3×C8C42×C5
FrattiniC22×C8C2×C5×D3
FittingC22×C3×C5×C16C2
socleC22×C3×C5#107
prime radicalC23×C3×C5Q16
cosocleC22×C3×C8C22×C5
hypercenterC22×C5×C16D3
hypocenterC3C5×#1381
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C22×C5×C16

256 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)(9,10,11,12)(13,15,18,29,17,28,32,43,19,30,33,44,31,42,16,27)(14,20,23,35,24,36,39,41,25,37,38,40,22,34,21,26);(7,8)(13,14,17,22,19,25,31,24)(15,26,28,40,30,41,42,35)(16,23,18,21,32,38,33,39)(20,29,34,43,37,44,36,27)

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, 4533);