Finite Group Databasebeta

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C5×C11×Dic51 #26014335

order11220
isoclinismisoclinic class of D51
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic51
unambiguous semidirect productC3⋊(C5×C11×Dic17)

Splittings

derived, HallC3×C17 ⋊ C4×C5×C11
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ C4×C11
HallC11×C17 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ Dic17
HallC5×C17 ⋊ C11×Dic3
HallC3×C11 ⋊ C5×Dic17
SylowC17 ⋊ C5×C11×Dic3
HallC3×C5 ⋊ C11×Dic17
SylowC3 ⋊ C5×C11×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D51
commutator, hypocenterC3×C17C4×C5×C11
FrattiniC2C5×C11×D51
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3×C17C2×C5×C11
LCSG ▷ C3×C17
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2970 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×Dic153, C5×C11×C3⋊Dic51, C3×C5×C11×Dic51
maximal normal subgroup ofC3×C5×C11×Dic51
maximal quotient ofC5×C11×Dic153, C5×C11×C3⋊Dic51, C3×C5×C11×Dic51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 11);