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C5×#68806 #14307368

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

Aliases

direct productC5×#68806

Splittings

HallC3×C5 ⋊ #1993
SylowC3 ⋊ C5×#1993

Subgroups

subgroupG/H
centerC23×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#340C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#340D3
hypocenterC3C5×#1993
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5 ◁ C5×#340

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(7,8)(13,15,16,20)(14,17,18,19)(22,26)(23,28);(6,7,8)(9,11,12,10)(21,23,27,22,25,28,24,26);(9,10,12,11)(13,14,16,18)(15,19,20,17)(21,22)(23,27)(24,28)(25,26)

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 33066);