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C5×#71998 #14294658

order1920
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#71998

Splittings

HallC3×C5 ⋊ #1738
SylowC3 ⋊ C5×#1738

Subgroups

subgroupG/H
centerC2×C4×C5C2×D12
commutatorC3×C4C2×C42×C5
FrattiniC22×C4C22×C5×D3
FittingC22×C3×C5×M16C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC24×C3×C5Q8
cosocleC22×C3×C4C23×C5
hypercenterC22×C5×M16D3
hypocenterC3C5×#1738
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C22×C5×M16

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 28 points:

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

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, 20356);