Finite Group Databasebeta

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C5×#69888 #14296008

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C22×C4

Aliases

direct productC5×#69888

Splittings

FittingC3×C5×#405 ⋊ C2
HallC3×C5 ⋊ #1765
SylowC3 ⋊ C5×#1765

Subgroups

subgroupG/H
centerC2×C4×C5C2×#67
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#405C2
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#405D3
hypocenterC3C5×#1765
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×C8 ◁ C5×#405

584 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)(13,15,17,25,18,23,16,24)(14,20,21,27,22,28,19,26);(7,8)(9,10,11,12)(14,19,22,21)(15,23)(20,27,28,26)(24,25);(7,8)(13,14,17,21,18,22,16,19)(15,20,25,27,23,28,24,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21706);