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C5×#72139 #14296862

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#72139

Splittings

HallC3×C5 ⋊ #1782
SylowC3 ⋊ C5×#1782

Subgroups

subgroupG/H
centerC22×C5C2×#217
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
Fitting, prime radicalC22×C3×C5×#41C2
socleC22×C3×C5C2×C22⋊C4
cosocleC24×C3C23×C5
hypercenterC22×C5×#41D3
hypocenterC3C5×#1782
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C22×C5×#41

1224 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)(10,12)(13,16,17,24)(14,19,20,26)(15,22,23,28)(18,25,21,27);(13,15)(14,18)(16,22)(17,23)(19,25)(20,21)(24,28)(26,27);(7,8)(9,10)(11,12)(13,14)(15,21,23,18)(16,19)(17,20)(22,27,28,25)(24,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 22560);