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C2×C5×D1547 #44525965

order30940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1547
unambiguous semidirect product(C2×C7)⋊(C5×D221)
unambiguous semidirect product(C2×C13)⋊(C5×D119)
unambiguous semidirect product(C2×C17)⋊(C5×D91)

Splittings

Fitting, socleC2×C5×C7×C13×C17 ⋊ C2
derived, HallC7×C13×C17 ⋊ C22×C5
HallC5×C7×C13×C17 ⋊ C22
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C5×D13
HallC7×C13 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×D91
HallC5×C13 ⋊ C2×D119
HallC5×C7 ⋊ C2×D221
SylowC17 ⋊ C2×C5×D91
SylowC13 ⋊ C2×C5×D119
SylowC7 ⋊ C2×C5×D221

Subgroups

subgroupG/H
center, hypercenterC2×C5D1547
commutator, cosocle, hypocenterC7×C13×C17C22×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C17C2
LCSG ▷ C7×C13×C17
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 15470

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

7750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 115);