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C5×#70598 #14313888

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#70598

Splittings

FittingC2×C3×C5×#107 ⋊ C2
HallC3×C5 ⋊ #2139
SylowC3 ⋊ C5×#2139

Subgroups

subgroupG/H
centerC22×C5C2×#213
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC2×C3×C5×#107C2
socleC22×C3×C5C2×D8
prime radicalC2×C5×#904C2
cosocleC2×C3×C8C23×C5
hypercenterC2×C5×#107D3
hypocenterC3C5×#2139
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×C8 ◁ C2×C5×#107

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39586);