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C5×#78626 #14414902

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#78626

Splittings

FittingC3×C5×#407 ⋊ C2
HallC3×C5 ⋊ #2929
SylowC3 ⋊ C5×#2929

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#407C2
socleC22×C3×C5C23×C4
prime radicalC5×#5791C2
cosocleC2×C3×C4C24×C5
hypercenterC5×#407D3
hypocenterC3C5×#2929
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×#407

1040 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 140600);