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C5×#70149 #14313717

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

Aliases

direct productC5×#70149

Splittings

FittingC3×C5×#413 ⋊ C2
HallC3×C5 ⋊ #2134
SylowC3 ⋊ C5×#2134

Subgroups

subgroupG/H
centerC2×C5C2×#806
commutatorC2×C3×C4C22×C4×C5
FrattiniC2×Q8C22×C5×D3
FittingC3×C5×#413C2
socleC2×C3×C5C2×#99
prime radicalC5×#5830C2
cosocleC2×C3×Q8C23×C5
hypercenterC5×#413D3
hypocenterC3C5×#2134
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#413

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 39415);