Finite Group Databasebeta

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C5×#70513 #14306030

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

Aliases

direct productC5×#70513

Splittings

FittingC3×C5×#423 ⋊ C2
HallC3×C5 ⋊ #1963
SylowC3 ⋊ C5×#1963

Subgroups

subgroupG/H
centerC2×C4×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#423C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5477C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#423D3
hypocenterC3C5×#1963
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#423

640 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)(9,10,11,12)(15,23)(19,27)(22,28)(24,25);(7,8)(13,15)(14,19,21,27)(16,24)(17,25)(18,23)(20,22,26,28);(10,12)(13,14,17,20,18,21,16,26)(15,22,25,27,23,28,24,19)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 31728);