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C5×#71853 #14302887

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71853

Splittings

HallC3×C5 ⋊ #1911
SylowC3 ⋊ C5×#1911

Subgroups

subgroupG/H
centerC2×C5#5220
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
Fitting, prime radicalC3×C5×#535C2
socleC2×C3×C5#386
cosocleC22×C3×C4C23×C5
hypercenterC5×#535D3
hypocenterC3C5×#1911
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#535

724 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)(10,16)(12,13)(15,23)(19,21);(7,8)(9,11)(10,15,16,23)(12,19)(13,21)(14,20)(17,18,22,24);(7,8)(9,10,13,17,14,16,12,22)(11,18,21,23,20,24,19,15)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28585);