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C11×C17×Dic15 #26014338

order11220
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×Dic15
unambiguous semidirect productC3⋊(C11×C17×Dic5)

Splittings

derived, HallC3×C5 ⋊ C4×C11×C17
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C17
HallC5×C17 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic3×C17
HallC3×C17 ⋊ C11×Dic5
HallC3×C11 ⋊ C17×Dic5
SylowC5 ⋊ C11×Dic3×C17
SylowC3 ⋊ C11×C17×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D15
commutator, hypocenterC3×C5C4×C11×C17
FrattiniC2C11×C17×D15
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3×C5C2×C11×C17
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C17×Dic45, C11×C17×C3⋊Dic15, C3×C11×C17×Dic15
maximal normal subgroup ofC3×C11×C17×Dic15
maximal quotient ofC11×C17×Dic45, C11×C17×C3⋊Dic15, C3×C11×C17×Dic15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 14);