Finite Group Databasebeta

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C5×#69889 #14296456

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

Aliases

direct productC5×#69889

Splittings

HallC3×C5 ⋊ #1772
SylowC3 ⋊ C5×#1772

Subgroups

subgroupG/H
centerC2×C5×C8#67
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#405C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C3×C4C23×C5
hypercenterC5×#405D3
hypocenterC3C5×#1772
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C8 ◁ C22×C5×C8 ◁ C5×#405

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 22154);