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C5×#82213 #14412540

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#82213

Splittings

FittingC2×C3×C5×#117 ⋊ C2
HallC3×C5 ⋊ #2896
SylowC3 ⋊ C5×#2896

Subgroups

subgroupG/H
centerC2×C4×C5C2×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#117C2
socleC22×C3×C5C22×D4
prime radicalC22×C5×#235C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#117D3
hypocenterC3C5×#2896
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×#117

1544 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)(13,16,18,17)(14,21,20,25)(15,23,24,26)(19,28,27,22);(14,20)(19,27)(21,25)(22,28);(7,8)(13,15)(14,19)(16,23)(17,26)(18,24)(20,27)(21,28)(22,25);(9,10,11,12)(13,14)(15,22)(16,21)(17,25)(18,20)(19,23)(24,28)(26,27)

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, 138238);