Finite Group Databasebeta

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C5×#69552 #14305923

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

Aliases

direct productC5×#69552

Splittings

HallC3×C5 ⋊ #1960
SylowC3 ⋊ C5×#1960

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#382C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#382D3
hypocenterC3C5×#1960
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C5×#382

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 31621);