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C2×C11×C5⋊D145 #44542127

order31900
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C11×C5⋊D145
unambiguous semidirect product(C2×C5)⋊(C11×D145)
unambiguous semidirect product(C2×C29)⋊(C11×C5⋊D5)

Splittings

Fitting, socleC2×C52×C11×C29 ⋊ C2
derived, HallC52×C29 ⋊ C22×C11
HallC52×C11×C29 ⋊ C22
HallC11×C29 ⋊ C2×C5⋊D5
HallC52×C11 ⋊ C2×D29
SylowC29 ⋊ C2×C11×C5⋊D5
SylowC52 ⋊ C2×C11×D29

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊D145
commutator, cosocle, hypocenterC52×C29C22×C11
FrattiniC1G
Fitting, socleC2×C52×C11×C29C2
LCSG ▷ C52×C29
UCSC1 ◁ C2×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 15950

A minimal faithful permutation representation — 3 generators on 52 points:

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

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 162);