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C7×#6127 #13089885

order1456
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×#6127

Splittings

FittingC2×C4×C7×C13 ⋊ C2
HallC7×C13 ⋊ #41
SylowC13 ⋊ C7×#41

Subgroups

subgroupG/H
centerC4×C7C2×D13
commutator, cosocleC2×C13C23×C7
FrattiniC2C22×C7×D13
FittingC2×C4×C7×C13C2
socleC2×C7×C13C23
hypercenterC2×C4×C7D13
hypocenterC13C7×#41
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C7 ◁ C2×C4×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 728

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 139);