Finite Group Databasebeta

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C5×#66930 #13183004

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#66930

Splittings

HallC5×C11 ⋊ #117
SylowC11 ⋊ C5×#117

Subgroups

subgroupG/H
centerC22×C5C22×D11
commutatorC2×C11C22×C4×C5
FrattiniC22C22×C5×D11
FittingC5×C11×C22⋊C4C2
socleC22×C5×C11C23
prime radicalC23×C5×C11C22
cosocleC22×C11C23×C5
hypercenterC5×C22⋊C4D11
hypocenterC11C5×#117
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C5 ◁ C5×C22⋊C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 880

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 813);