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C5×#69033 #14299867

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#69033

Splittings

FittingC3×C5×#344 ⋊ C2
HallC3×C5 ⋊ #1861
SylowC3 ⋊ C5×#1861

Subgroups

subgroupG/H
centerC4×C5#882
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#344C2
socleC2×C3×C5#385
prime radicalC2×C5×#235C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#344D3
hypocenterC3C5×#1861
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#344

524 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25565);