Finite Group Databasebeta

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C5×#84111 #14412716

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#84111

Splittings

HallC3×C5 ⋊ #2898
SylowC3 ⋊ C5×#2898

Subgroups

subgroupG/H
centerC22×C5C22×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
Fitting, prime radicalC2×C3×C5×2−1+4C2
socleC22×C3×C5C22×D4
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×2−1+4D3
hypocenterC3C5×#2898
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41 ◁ C2×C5×2−1+4

1452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

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, 138414);