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C5×C11×Dic3×C17 #26014334

order11220
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic3×C17
unambiguous semidirect productC3⋊(C4×C5×C11×C17)

Splittings

derived, SylowC3 ⋊ C4×C5×C11×C17
HallC3×C5×C11×C17 ⋊ C4
HallC3×C11×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C17
HallC3×C17 ⋊ C4×C5×C11
HallC3×C11 ⋊ C4×C5×C17
HallC3×C5 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C17D3
commutator, hypocenterC3C4×C5×C11×C17
FrattiniC2C5×D3×C11×C17
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3C2×C5×C11×C17
LCSG ▷ C3
UCSC1 ◁ C2×C5×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5610 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×C17×Dic9, C5×C11×C17×C3⋊Dic3, C3×C5×C11×Dic3×C17
maximal normal subgroup ofC3×C5×C11×Dic3×C17
maximal quotient ofC5×C11×C17×Dic9, C5×C11×C17×C3⋊Dic3, C3×C5×C11×Dic3×C17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 10);