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C5×#70394 #14309018

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

Aliases

direct productC5×#70394

Splittings

HallC3×C5 ⋊ #2031
SylowC3 ⋊ C5×#2031

Subgroups

subgroupG/H
centerC4×C5#936
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#421C2
socleC2×C3×C5#393
prime radicalC2×C3×C5×#41C22
hypercenterC5×#421D3
hypocenterC3C5×#2031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#421

488 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)(10,15)(12,19)(13,21)(14,20)(16,24)(17,23)(18,22);(7,8)(11,19,20,21)(15,18,23,24);(9,10)(11,18,20,24)(12,16)(13,22)(14,17)(15,21,23,19)

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34716);