Finite Group Databasebeta

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C3×C11×Dic65 #22575037

order8580
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic65

Splittings

derived, HallC5×C13 ⋊ C3×C4×C11
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ C4×C11
HallC3×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C3×Dic5
HallC5×C11 ⋊ C3×Dic13
HallC3×C13 ⋊ C11×Dic5
HallC3×C5 ⋊ C11×Dic13
SylowC13 ⋊ C3×C11×Dic5
SylowC5 ⋊ C3×C11×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D65
commutator, hypocenterC5×C13C3×C4×C11
FrattiniC2C3×C11×D65
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C11×Dic65, C11×Dic65⋊C9, C3×C11×Dic65⋊C3, …
maximal normal subgroup ofC9×C11×Dic65, C11×Dic65⋊C9, C3×C11×Dic65⋊C3, …
maximal quotient ofC9×C11×Dic65, C3×C11×Dic195, C32×C11×Dic65

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 9);