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C11×C3⋊Dic15 #14520429

order1980
isoclinismisoclinic class of C3⋊D15
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊Dic15
unambiguous semidirect productC3⋊(C11×Dic15)

Splittings

derived, HallC32×C5 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4
HallC32×C11 ⋊ Dic5
HallC5×C11 ⋊ C3⋊Dic3
SylowC32 ⋊ C11×Dic5
SylowC5 ⋊ C11×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D15
commutator, hypocenterC32×C5C4×C11
FrattiniC2C11×C3⋊D15
Fitting, socle, prime radicalC2×C32×C5×C11C2
cosocleC2×C32×C5C2×C11
LCSG ▷ C32×C5
UCSC1 ◁ C2×C11

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C11×C3⋊Dic15, C11×C3⋊Dic105, C121×C3⋊Dic15, …
maximal normal subgroup ofC7×C11×C3⋊Dic15, C121×C3⋊Dic15, C112×C3⋊Dic15, …
maximal quotient ofC7×C11×C3⋊Dic15, C11×C3⋊Dic105, C121×C3⋊Dic15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 54);