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C5×#78980 #14418107

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

Aliases

direct productC5×#78980

Splittings

FittingC2×C3×C5×#104 ⋊ C2
HallC3×C5 ⋊ #2956
SylowC3 ⋊ C5×#2956

Subgroups

subgroupG/H
centerC4×C5C2×D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#104C2
socleC2×C3×C5C2×C4×D4
prime radicalC5×#5822C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#104D3
hypocenterC3C5×#2956
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#104

916 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 143805);