Finite Group Databasebeta

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C3×C17×Dic55 #26014332

order11220
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic55
unambiguous semidirect productC11⋊(C3×C17×Dic5)

Splittings

derived, HallC5×C11 ⋊ C3×C4×C17
HallC3×C5×C11×C17 ⋊ C4
HallC5×C11×C17 ⋊ C3×C4
HallC3×C11×C17 ⋊ Dic5
HallC3×C5×C17 ⋊ Dic11
HallC11×C17 ⋊ C3×Dic5
HallC3×C5×C11 ⋊ C4×C17
HallC5×C17 ⋊ C3×Dic11
HallC3×C11 ⋊ C17×Dic5
HallC3×C5 ⋊ C17×Dic11
SylowC11 ⋊ C3×C17×Dic5
SylowC5 ⋊ C3×C17×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D55
commutator, hypocenterC5×C11C3×C4×C17
FrattiniC2C3×C17×D55
Fitting, socle, prime radicalC2×C3×C5×C11×C17C2
cosocleC2×C5×C11C2×C3×C17
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2958 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C17×Dic55, C3×C17×Dic165, C32×C17×Dic55
maximal normal subgroup ofC9×C17×Dic55, C32×C17×Dic55
maximal quotient ofC9×C17×Dic55, C3×C17×Dic165, C32×C17×Dic55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 8);