Finite Group Databasebeta

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C5×#69574 #14298814

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

Aliases

direct productC5×#69574

Splittings

HallC3×C5 ⋊ #1834
SylowC3 ⋊ C5×#1834

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#384C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#384D3
hypocenterC3C5×#1834
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C5×#384

496 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)(6,7)(14,18)(17,20)(21,23,24,22,26,27,25,28);(7,8)(13,15,16,19)(14,17,18,20)(21,22,25,23,26,28,24,27);(9,10,11,12)(13,14)(15,17)(16,18)(19,20)(22,27)(23,28)(24,25)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24512);