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C7×#4094 #11765192

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

Aliases

direct productC7×#4094

Splittings

HallC5×C7 ⋊ #131
SylowC5 ⋊ C7×#131

Subgroups

subgroupG/H
centerC4×C7C22×D5
commutatorC2×C5C22×C4×C7
FrattiniC4C22×C7×D5
Fitting, prime radicalC5×C7×#41C2
socleC2×C5×C7C22×C4
cosocleC4×C5C23×C7
hypercenterC7×#41D5
hypocenterC5C7×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C7 ◁ C7×#41

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

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, 798);