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C13×Dic165 #22575046

order8580
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic165
unambiguous semidirect productC3⋊(C13×Dic55)
unambiguous semidirect productC11⋊(C13×Dic15)

Splittings

derived, HallC3×C5×C11 ⋊ C4×C13
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ Dic11
HallC11×C13 ⋊ Dic15
HallC5×C13 ⋊ Dic33
HallC5×C11 ⋊ Dic3×C13
HallC3×C13 ⋊ Dic55
HallC3×C11 ⋊ C13×Dic5
HallC3×C5 ⋊ C13×Dic11
SylowC11 ⋊ C13×Dic15
SylowC5 ⋊ C13×Dic33
SylowC3 ⋊ C13×Dic55

Subgroups

subgroupG/H
center, hypercenterC2×C13D165
commutator, hypocenterC3×C5×C11C4×C13
FrattiniC2C13×D165
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×Dic495, C13⋊C3×Dic165, C13×C3⋊Dic165, …
maximal normal subgroup ofC13⋊C3×Dic165, C3×C13×Dic165
maximal quotient ofC13×Dic495, C13×C3⋊Dic165, C3×C13×Dic165

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 18);