Finite Group Databasebeta

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C5×#83231 #14331238

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

Aliases

direct productC5×#83231

Splittings

HallC3×C5 ⋊ #2381
SylowC3 ⋊ C5×#2381

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC2×C3×C5×C4⋊Q8C2
socle, prime radicalC23×C3×C5C24
cosocleC23×C3C24×C5
hypercenterC2×C5×C4⋊Q8D3
hypocenterC3C5×#2381
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C5×C4⋊Q8

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2,3,4,5)(6,7,8)(14,18)(17,19)(21,24,25,33)(22,28,27,35)(23,30,31,32)(26,34,29,36);(13,15,16,20)(14,17,18,19)(22,27)(26,29)(28,35)(34,36);(15,20)(17,19)(21,23,25,31)(22,26,27,29)(24,32,33,30)(28,36,35,34);(7,8)(9,10,11,12)(13,14)(15,19)(16,18)(17,20)(21,22)(23,29)(24,28)(25,27)(26,31)(30,36)(32,34)(33,35)

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, 56936);