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C5×C3⋊Dic33 #14520428

order1980
isoclinismisoclinic class of C3⋊D33
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊Dic33
unambiguous semidirect productC3⋊(C5×Dic33)

Splittings

derived, HallC32×C11 ⋊ C4×C5
HallC32×C5×C11 ⋊ C4
HallC5×C11 ⋊ C3⋊Dic3
HallC32×C5 ⋊ Dic11
SylowC11 ⋊ C5×C3⋊Dic3
SylowC32 ⋊ C5×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D33
commutator, hypocenterC32×C11C4×C5
FrattiniC2C5×C3⋊D33
Fitting, socle, prime radicalC2×C32×C5×C11C2
cosocleC2×C32×C11C2×C5
LCSG ▷ C32×C11
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1980

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19,20)(22,23)(25,26);(6,7,9,11,13,15,16,14,12,10,8)(24,25,26);(21,22,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C7×C3⋊Dic33, C5×C3⋊Dic231, C5×C3⋊Dic363, …
maximal normal subgroup ofC5×C7×C3⋊Dic33, C5×C11×C3⋊Dic33, C5×C13×C3⋊Dic33, …
maximal quotient ofC5×C7×C3⋊Dic33, C5×C3⋊Dic231, C5×C3⋊Dic363, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 53);