Finite Group Databasebeta

← Prev (#11765076) Next (#11765078) →

C5×#6482 #11765077

order1120
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#6482

Splittings

FittingC5×C7×Q16 ⋊ C2
HallC5×C7 ⋊ #135
SylowC7 ⋊ C5×#135

Subgroups

subgroupG/H
centerC2×C5D4×D7
commutator, cosocleC4×C7C23×C5
FrattiniC4C22×C5×D7
FittingC5×C7×Q16C2
socleC2×C5×C7C2×D4
hypercenterC5×Q16D7
hypocenterC7C5×#135
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q16

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 560

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

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

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 683);