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C11×Dic255 #26014339

order11220
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic255
unambiguous semidirect productC3⋊(C11×Dic85)

Splittings

derived, HallC3×C5×C17 ⋊ C4×C11
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ Dic5
HallC11×C17 ⋊ Dic15
HallC3×C5×C11 ⋊ Dic17
HallC5×C17 ⋊ C11×Dic3
HallC5×C11 ⋊ Dic51
HallC3×C17 ⋊ C11×Dic5
HallC3×C11 ⋊ Dic85
SylowC17 ⋊ C11×Dic15
HallC3×C5 ⋊ C11×Dic17
SylowC5 ⋊ C11×Dic51
SylowC3 ⋊ C11×Dic85

Subgroups

subgroupG/H
center, hypercenterC2×C11D255
commutator, hypocenterC3×C5×C17C4×C11
FrattiniC2C11×D255
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3×C5×C17C2×C11
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2838 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×Dic765, C11×C3⋊Dic255, C3×C11×Dic255
maximal normal subgroup ofC3×C11×Dic255
maximal quotient ofC11×Dic765, C11×C3⋊Dic255, C3×C11×Dic255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 15);