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C5×#68989 #14294773

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#68989

Splittings

FittingC3×C5×#343 ⋊ C2
HallC3×C5 ⋊ #1742
SylowC3 ⋊ C5×#1742

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC22×C3C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#343C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C5×D3C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC5×#343D3
hypocenterC3C5×#1742
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#343

776 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)(7,8)(13,16,18,17)(14,20,21,22)(15,24,25,26)(19,27,23,28);(6,7,8)(9,10,11,12)(13,15)(14,19)(16,24)(17,26)(18,25)(20,27)(21,23)(22,28);(13,14,17,22,18,21,16,20)(15,23,24,28,25,19,26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20471);