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C5×#69794 #14305226

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#69794

Splittings

HallC3×C5 ⋊ #1945
SylowC3 ⋊ C5×#1945

Subgroups

subgroupG/H
centerC2×C4×C5C2×D12
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socleC22×C3×C5C4×D4
prime radicalC23×C3×C5#41
cosocleC22×C3×C4C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C5×#1945
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C5×C8 ◁ C2×C4×C5×C8

416 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)(13,16,17,25,19,24,18,15)(14,21,22,26,23,20,27,28);(10,12)(13,15,18,24,19,25,17,16)(14,20,22,28,23,21,27,26);(7,8)(9,10)(11,12)(13,14,18,22,19,23,17,27)(15,20,24,28,25,21,16,26)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30924);