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C5×D23×D77 #47978436

order35420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D23×D77
unambiguous semidirect product(C7×D23)⋊(C5×D11)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C22
derived, HallC7×C11×C23 ⋊ C22×C5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×C5×D11
HallC5×C23 ⋊ C2×D77
HallC7×C11 ⋊ C2×C5×D23
HallC5×C11 ⋊ D7×D23
HallC5×C7 ⋊ D11×D23
SylowC23 ⋊ C2×C5×D77
SylowC11 ⋊ C5×D7×D23
SylowC7 ⋊ C5×D11×D23

Subgroups

subgroupG/H
center, hypercenterC5D23×D77
commutator, cosocle, hypocenterC7×C11×C23C22×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C23C22
LCSG ▷ C7×C11×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 8855

A minimal faithful permutation representation — 2 generators on 46 points:

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

Conjugacy classes & character table

2600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 70);