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C5×#69175 #14315361

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

Aliases

direct productC5×#69175

Splittings

HallC3×C5 ⋊ C4×SD32
SylowC3 ⋊ C4×C5×SD32

Subgroups

subgroupG/H
centerC22×C5D3×D8
commutatorC3×C8C22×C4×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×C3×C5×D8C22
cosocleC2×C3×C8C23×C5
hypercenterC5×#357D3
hypocenterC3C4×C5×SD32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8 ◁ C5×#357

324 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)(9,11,12,10);(7,8)(13,14,17,20)(15,22,24,28)(16,25,23,19)(18,26,27,21);(7,8)(9,10,12,11)(14,18)(15,21)(16,23)(19,28)(20,27)(22,25)(24,26)

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, 41059);