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C5×#69863 #14284077

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

Aliases

direct productC5×#69863

Splittings

HallC3×C5 ⋊ #1528
SylowC3 ⋊ C5×#1528

Subgroups

subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C4×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C42C23×C5
hypercenterC4×C5×M16D3
hypocenterC3C5×#1528
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C4×C5×M16

424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(18,23)(22,25)(24,31)(30,32);(7,8)(9,10)(11,15)(12,14)(13,16)(17,19,21,27)(18,22,23,25)(20,28,29,26)(24,32,31,30);(10,13,14,15)(17,18,20,24,21,23,29,31)(19,25,26,32,27,22,28,30)

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, 9775);