Finite Group Databasebeta

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C5×#75987 #14329821

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#75987

Splittings

HallC3×C5 ⋊ #2369
SylowC3 ⋊ C5×#2369

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#389C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC5×#389D3
hypocenterC3C5×#2369
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#389

992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 28 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 55519);