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C7×#3832 #11759692

order1008
automorphism?
homologyAbelianization (H1) = C23×C7 · Schur multiplier (H2) = C22×C3

Aliases

direct productC7×#3832

Splittings

FittingC32×C7×Q8 ⋊ C2
HallC32×C7 ⋊ #41
SylowC32 ⋊ C7×#41

Subgroups

subgroupG/H
centerC2×C7C22×C3⋊D3
commutator, cosocleC2×C32C23×C7
FrattiniC2C22×C7×C3⋊D3
FittingC32×C7×Q8C2
socleC2×C32×C7C23
hypercenterC7×Q8C3⋊D3
hypocenterC32C7×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C7 ◁ C7×Q8

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 504

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2,3,4,5,6,7)(8,10,11,14)(9,12,13,15)(19,20,21);(8,9,11,13)(10,15,14,12)(16,17,18);(10,14)(12,15)(17,18)(20,21)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 863);