Finite Group Databasebeta

← Prev (#11765150) Next (#11765152) →

C7×#4053 #11765151

order1120
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×#4053

Splittings

FittingC5×C7×M16 ⋊ C2
HallC5×C7 ⋊ #131
SylowC5 ⋊ C7×#131

Subgroups

subgroupG/H
centerC4×C7C22×D5
commutatorC2×C5C22×C4×C7
FrattiniC4C22×C7×D5
FittingC5×C7×M16C2
socleC2×C5×C7C22×C4
prime radicalC7×#709C2
cosocleC4×C5C23×C7
hypercenterC7×M16D5
hypocenterC5C7×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C7 ◁ C7×M16

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 757);