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C5×#70057 #14313257

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

Aliases

direct productC5×#70057

Splittings

FittingC3×C5×#410 ⋊ C2
HallC3×C5 ⋊ #2122
SylowC3 ⋊ C5×#2122

Subgroups

subgroupG/H
centerC2×C5C2×#806
commutatorC23×C3C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×#410C2
socleC2×C3×C5C2×#99
prime radicalC5×#5830C2
cosocleC2×C3×D4C23×C5
hypercenterC5×#410D3
hypocenterC3C5×#2122
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#410

532 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)(9,11,13,17)(10,15,16,23)(12,18,20,24)(14,21,19,22);(7,8)(10,14)(11,17)(15,22)(16,19)(18,24)(21,23);(9,10)(11,15)(12,19,20,14)(13,16)(17,23)(18,22,24,21)

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, 38955);