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C2×C9×C5⋊(C13⋊D13) #44477792

order30420
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C9×C5⋊(C13⋊D13)
unambiguous semidirect product(C2×C5)⋊(C9×C13⋊D13)

Splittings

FittingC2×C5×C9×C132 ⋊ C2
derived, HallC5×C132 ⋊ C22×C9
HallC5×C9×C132 ⋊ C22
HallC9×C132 ⋊ C2×D5
SylowC132 ⋊ C2×C9×D5
HallC5×C9 ⋊ C2×C13⋊D13
SylowC5 ⋊ C2×C9×C13⋊D13

Subgroups

subgroupG/H
center, hypercenterC2×C9C5⋊(C13⋊D13)
commutator, hypocenterC5×C132C22×C9
FrattiniC3C2×C3×C5⋊(C13⋊D13)
FittingC2×C5×C9×C132C2
socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5⋊(C13⋊D13)C3
cosocleC3×C5×C132C22×C3
LCSG ▷ C5×C132
UCSC1 ◁ C2×C9

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 15210

A minimal faithful permutation representation — 3 generators on 42 points:

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

Conjugacy classes & character table

7632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 381);