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C2×C5×#16809817 #46776508

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#16809817

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C22×C3×C5
HallC2×C5×D559 ⋊ C3
HallC5×#13131976 ⋊ C22
HallC5×C13×C43 ⋊ C22×C3
HallC2×D559 ⋊ C3×C5
Hall#13131976 ⋊ C22×C5
HallC5×C43 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×D43⋊C3
SylowC43 ⋊ C2×C5×D13⋊C3
SylowC13 ⋊ C2×C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#16809817
commutator, cosocle, hypocenterC13×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 5590

A minimal faithful permutation representation — 2 generators on 63 points:

(3,4,5,6,7)(9,13,14,10,11,15)(12,19,18,16,17,20)(22,26,27,23,24,28)(25,34,35,29,30,44)(31,47,48,37,38,56)(32,46,42,40,36,33)(39,52,54,43,45,57)(41,58,59,50,49,53)(51,61,62,60,55,63);(1,2)(8,9,12,11,15,18,17,19,20,14,13,16,10)(21,22,25,31,39,42,27,26,32,41,51,59,35,46,34,45,55,62,48,57,58,47,38,49,54,56,63,61,52,30,36,44,53,60,50,40,24,28,33,43,37,29,23)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 128);