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C5×D3367 #46797604

order33670
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3367
unambiguous semidirect productC7⋊(C5×D481)
unambiguous semidirect productC13⋊(C5×D259)
unambiguous semidirect productC37⋊(C5×D91)

Splittings

Fitting, socle, HallC5×C7×C13×C37 ⋊ C2
derived, HallC7×C13×C37 ⋊ C2×C5
HallC5×C13×C37 ⋊ D7
HallC5×C7×C37 ⋊ D13
HallC13×C37 ⋊ C5×D7
HallC5×C7×C13 ⋊ D37
HallC7×C37 ⋊ C5×D13
HallC5×C37 ⋊ D91
HallC7×C13 ⋊ C5×D37
HallC5×C13 ⋊ D259
SylowC37 ⋊ C5×D91
HallC5×C7 ⋊ D481
SylowC13 ⋊ C5×D259
SylowC7 ⋊ C5×D481

Subgroups

subgroupG/H
center, hypercenterC5D3367
commutator, cosocle, hypocenterC7×C13×C37C2×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C37C2
LCSG ▷ C7×C13×C37
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 16835

A minimal faithful permutation representation — 2 generators on 62 points:

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

Conjugacy classes & character table

8425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33670, 8);