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C7×#63252 #14274158

order1904
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C23×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×#63252

Splittings

FittingC2×C4×C7×C17 ⋊ C2
HallC7×C17 ⋊ #41
SylowC17 ⋊ C7×#41

Subgroups

subgroupG/H
centerC4×C7C2×D17
commutator, cosocleC2×C17C23×C7
FrattiniC2C22×C7×D17
FittingC2×C4×C7×C17C2
socleC2×C7×C17C23
hypercenterC2×C4×C7D17
hypocenterC17C7×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C7 ◁ C2×C4×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 952

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7)(8,9,11,13,15,17,19,21,23,24,22,20,18,16,14,12,10)(26,30)(29,32);(25,27,28,31)(26,29,30,32);(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,29)(28,30)(31,32)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1904, 141);