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C2×C7×D1173 #45659335

order32844
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D1173
unambiguous semidirect product(C2×C3)⋊(C7×D391)
unambiguous semidirect product(C2×C17)⋊(C7×D69)
unambiguous semidirect product(C2×C23)⋊(C7×D51)

Splittings

Fitting, socleC2×C3×C7×C17×C23 ⋊ C2
derived, HallC3×C17×C23 ⋊ C22×C7
HallC3×C7×C17×C23 ⋊ C22
HallC7×C17×C23 ⋊ C2×D3
HallC3×C7×C23 ⋊ C2×D17
HallC17×C23 ⋊ C2×D3×C7
HallC3×C7×C17 ⋊ C2×D23
HallC7×C23 ⋊ C2×D51
HallC7×C17 ⋊ C2×D69
HallC3×C23 ⋊ C2×C7×D17
HallC3×C17 ⋊ C2×C7×D23
SylowC23 ⋊ C2×C7×D51
HallC3×C7 ⋊ C2×D391
SylowC17 ⋊ C2×C7×D69
SylowC3 ⋊ C2×C7×D391

Subgroups

subgroupG/H
center, hypercenterC2×C7D1173
commutator, cosocle, hypocenterC3×C17×C23C22×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C17×C23C2
LCSG ▷ C3×C17×C23
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 16422

A minimal faithful permutation representation — 2 generators on 52 points:

(4,5)(6,7,8,9,10,11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52);(1,2)(3,4,5)(13,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15)(30,31,33,35,37,39,41,43,45,47,49,51,52,50,48,46,44,42,40,38,36,34,32)

Conjugacy classes & character table

8232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 100);