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C5×#70345 #14301474

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#70345

Splittings

HallC3×C5 ⋊ #1886
SylowC3 ⋊ C5×#1886

Subgroups

subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#419C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#419D3
hypocenterC3C5×#1886
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#419

648 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)(13,16,18,20)(14,15,23,27)(17,24,19,28)(21,26,22,25);(6,7,8)(9,11,12,10)(13,15)(14,20)(16,23)(17,26)(18,27)(19,25)(21,28)(22,24);(9,10,12,11)(13,14,19,22,18,23,17,21)(15,24,26,20,27,28,25,16)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27172);