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C5×#71723 #14301441

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71723

Splittings

HallC3×C5 ⋊ #1885
SylowC3 ⋊ C5×#1885

Subgroups

subgroupG/H
centerC22×C5#937
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#124C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#124D3
hypocenterC3C5×#1885
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#124

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 27139);