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C5×#78774 #14417156

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

Aliases

direct productC5×#78774

Splittings

FittingC2×C3×C5×#103 ⋊ C2
HallC3×C5 ⋊ #2947
SylowC3 ⋊ C5×#2947

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#103C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#103D3
hypocenterC3C5×#2947
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#103

940 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

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

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

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, 142854);