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C5×C17×Dic33 #26014336

order11220
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×Dic33
unambiguous semidirect productC3⋊(C5×C17×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C5×C17
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ Dic3
HallC3×C11×C17 ⋊ C4×C5
HallC3×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ C4×C17
HallC5×C11 ⋊ Dic3×C17
HallC3×C17 ⋊ C5×Dic11
HallC3×C5 ⋊ C17×Dic11
SylowC11 ⋊ C5×Dic3×C17
SylowC3 ⋊ C5×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D33
commutator, hypocenterC3×C11C4×C5×C17
FrattiniC2C5×C17×D33
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C3×C11C2×C5×C17
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C17×Dic99, C5×C17×C3⋊Dic33, C3×C5×C17×Dic33
maximal normal subgroup ofC3×C5×C17×Dic33
maximal quotient ofC5×C17×Dic99, C5×C17×C3⋊Dic33, C3×C5×C17×Dic33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 12);