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C5×D33⋊C4 #13050350

order1320
isoclinismisoclinic class of D3×D11
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D33⋊C4

Splittings

derived, HallC3×C11 ⋊ C2×C4×C5
HallC3×C5×C11 ⋊ C2×C4
HallC5×C11 ⋊ C4×D3
HallC3×C5 ⋊ C4×D11
SylowC11 ⋊ C4×C5×D3
SylowC3 ⋊ C4×C5×D11

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×D11
commutator, hypocenterC3×C11C2×C4×C5
FrattiniC2C5×D3×D11
Fitting, socleC2×C3×C5×C11C22
prime radicalC2×C5×D33C2
cosocleC2×C3×C11C22×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×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)(6,7,9,11,13,15,16,14,12,10,8)(18,19)(20,22,23,21);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19)(20,21,23,22)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 54);