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C5×#69954 #14299519

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#69954

Splittings

HallC3×C5 ⋊ #1855
SylowC3 ⋊ C5×#1855

Subgroups

subgroupG/H
centerC2×C4×C5C2×D12
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5C2×C4⋊C4
prime radicalC24×C3×C5Q8
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×C22⋊C8D3
hypocenterC3C5×#1855
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ C2×C5×C22⋊C8

556 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)(10,12);(7,8)(13,15,17,23,18,24,16,26)(14,19,20,27,21,28,25,22);(7,8)(9,10)(11,12)(13,14,17,20,18,21,16,25)(15,22,23,19,24,27,26,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25217);