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C11×C19×Dic15 #27159986

order12540
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC11×C19×Dic15
unambiguous semidirect productC3⋊(C11×C19×Dic5)

Splittings

derived, HallC3×C5 ⋊ C4×C11×C19
HallC3×C5×C11×C19 ⋊ C4
HallC5×C11×C19 ⋊ Dic3
HallC3×C11×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C19
HallC5×C19 ⋊ C11×Dic3
HallC3×C19 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic3×C19
HallC3×C11 ⋊ C19×Dic5
SylowC5 ⋊ C11×Dic3×C19
SylowC3 ⋊ C11×C19×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19D15
commutator, hypocenterC3×C5C4×C11×C19
FrattiniC2C11×C19×D15
Fitting, socle, prime radicalC2×C3×C5×C11×C19C2
cosocleC2×C3×C5C2×C11×C19
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3762 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C19×Dic45, C11×C19⋊C3×Dic15, C11×C19×C3⋊Dic15, …
maximal normal subgroup ofC11×C19⋊C3×Dic15, C3×C11×C19×Dic15
maximal quotient ofC11×C19×Dic45, C11×C19×C3⋊Dic15, C3×C11×C19×Dic15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 16);