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C5×#79423 #14415427

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

Aliases

direct productC5×#79423

Splittings

FittingC3×C5×C8×D4 ⋊ C2
HallC3×C5 ⋊ #2933
SylowC3 ⋊ C5×#2933

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×C8×D4C2
socleC22×C3×C5C23×C4
prime radicalC5×#5547C2
cosocleC2×C3×C4C24×C5
hypercenterC5×C8×D4D3
hypocenterC3C5×#2933
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C5×C8×D4

1004 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)(7,8)(15,21)(18,24)(22,27)(25,28);(6,7,8)(13,15,16,22,17,21,23,27)(14,18,19,25,20,24,26,28);(10,12);(9,10)(11,12)(13,14,16,19,17,20,23,26)(15,18,22,25,21,24,27,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141125);