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C5×Dic561 #26014337

order11220
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic561
unambiguous semidirect productC3⋊(C5×Dic187)

Splittings

derived, HallC3×C11×C17 ⋊ C4×C5
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic3
HallC3×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ Dic17
HallC5×C17 ⋊ Dic33
HallC5×C11 ⋊ Dic51
HallC3×C17 ⋊ C5×Dic11
HallC3×C11 ⋊ C5×Dic17
SylowC17 ⋊ C5×Dic33
HallC3×C5 ⋊ Dic187
SylowC11 ⋊ C5×Dic51
SylowC3 ⋊ C5×Dic187

Subgroups

subgroupG/H
center, hypercenterC2×C5D561
commutator, hypocenterC3×C11×C17C4×C5
FrattiniC2C5×D561
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3×C11×C17C2×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×Dic1683, C5×C3⋊Dic561, C3×C5×Dic561
maximal normal subgroup ofC3×C5×Dic561
maximal quotient ofC5×Dic1683, C5×C3⋊Dic561, C3×C5×Dic561

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 13);