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C2×C7×D1209 #46799641

order33852
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D1209
unambiguous semidirect product(C2×C3)⋊(C7×D403)
unambiguous semidirect product(C2×C13)⋊(C7×D93)
unambiguous semidirect product(C2×C31)⋊(C7×D39)

Splittings

Fitting, socleC2×C3×C7×C13×C31 ⋊ C2
derived, HallC3×C13×C31 ⋊ C22×C7
HallC3×C7×C13×C31 ⋊ C22
HallC7×C13×C31 ⋊ C2×D3
HallC3×C7×C31 ⋊ C2×D13
HallC13×C31 ⋊ C2×D3×C7
HallC3×C7×C13 ⋊ C2×D31
HallC7×C31 ⋊ C2×D39
HallC3×C31 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×D93
HallC3×C13 ⋊ C2×C7×D31
SylowC31 ⋊ C2×C7×D39
HallC3×C7 ⋊ C2×D403
SylowC13 ⋊ C2×C7×D93
SylowC3 ⋊ C2×C7×D403

Subgroups

subgroupG/H
center, hypercenterC2×C7D1209
commutator, cosocle, hypocenterC3×C13×C31C22×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C13×C31C2
LCSG ▷ C3×C13×C31
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 16926

A minimal faithful permutation representation — 2 generators on 56 points:

(4,5)(6,7,8,9,10,11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56);(1,2)(3,4,5)(13,14,16,18,20,22,24,25,23,21,19,17,15)(26,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28)

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 436);