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C2×C13×C5⋊#64424 #50304308

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C5⋊#64424
unambiguous semidirect product(C2×C5)⋊(C13×#64424)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ C2×C3
derived, HallC5×C72 ⋊ C22×C3×C13
HallC2×C13×C5⋊(C7⋊D7) ⋊ C3
HallC5×C13×#3861 ⋊ C22
HallC5×C72×C13 ⋊ C22×C3
HallC13×#3861 ⋊ C2×D5
HallC2×C5⋊(C7⋊D7) ⋊ C3×C13
HallC5×#3861 ⋊ C22×C13
HallC72×C13 ⋊ C2×C3×D5
Hall#3861 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×#64424
SylowC72 ⋊ C2×C3×D5×C13
SylowC5 ⋊ C2×C13×#64424

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊#64424
commutator, cosocle, hypocenterC5×C72C22×C3×C13
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C2×C13

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 6370

A minimal faithful permutation representation — 3 generators on 34 points:

(4,5)(6,7)(9,12,13,10,11,14)(16,19,20,17,18,21)(22,23,24,25,26,27,28,29,30,31,32,33,34);(1,2)(3,4,6,7,5)(15,16,18,21,20,19,17);(8,9,11,14,13,12,10)

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 994);