Finite Group Databasebeta

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C5×#74161 #14331285

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#74161

Splittings

HallC3×C5 ⋊ #2382
SylowC3 ⋊ C5×#2382

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#382C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC5×#382D3
hypocenterC3C5×#2382
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#382

816 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)(13,15,16,19)(14,18,17,20)(21,24,25,28)(22,26,23,27);(14,17)(18,20)(21,23,25,22)(24,27,28,26);(7,8)(13,14)(15,20)(16,17)(18,19)(21,22,25,23)(24,27,28,26);(9,10,11,12)(14,17)(15,19)(22,23)(26,27)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 56983);