Finite Group Databasebeta

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C5×#71580 #14294555

order1920
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#71580

Splittings

HallC3×C5 ⋊ #1735
SylowC3 ⋊ C5×#1735

Subgroups

subgroupG/H
centerC22×C4×C5#67
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#117C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#1735
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×#117

848 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)(18,24,26,25)(19,28,30,29)(23,31,32,27);(7,8)(13,14,15,16)(17,19,21,29,22,30,20,28)(18,23,24,31,26,32,25,27);(9,10,11,12)(17,18)(19,27)(20,24)(21,25)(22,26)(23,28)(29,32)(30,31)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20253);