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C3×C5×D44 #13050393

order1320
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D44
unambiguous semidirect productC4⋊(C3×C5×D11)

Splittings

FittingC3×C4×C5×C11 ⋊ C2
HallC3×C5×C11 ⋊ D4
HallC5×C11 ⋊ C3×D4
HallC3×C11 ⋊ C5×D4
SylowC11 ⋊ C3×C5×D4

Subgroups

subgroupG/H
centerC2×C3×C5C2×D11
commutator, cosocleC2×C11C22×C3×C5
FrattiniC2C2×C3×C5×D11
FittingC3×C4×C5×C11C2
socleC2×C3×C5×C11C22
hypercenterC3×C4×C5D11
hypocenterC11C3×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C3×C5 ◁ C3×C4×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3)(4,5,6,7,8)(9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23);(10,12)(14,23)(15,22)(16,21)(17,20)(18,19)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 97);