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C11×Dic5×C13⋊C3 #22575058

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

Aliases

direct productC11×Dic5×C13⋊C3
unambiguous semidirect product(C13×Dic5)⋊(C3×C11)
unambiguous semidirect product(C11×C13×Dic5)⋊C3

Splittings

derived, HallC5×C13 ⋊ C3×C4×C11
HallC11×C13×Dic5 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallC13×Dic5 ⋊ C3×C11
HallC5×C13⋊C3 ⋊ C4×C11
HallC11×C13 ⋊ C3×Dic5
HallC5×C11 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C11×Dic5
SylowC5 ⋊ C4×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11D5×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C11
FrattiniC2D5×C11×C13⋊C3
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

616 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×Dic5×C13⋊C3, C11×C13⋊C3×Dic15
maximal normal subgroup ofC3×C11×Dic5×C13⋊C3
maximal quotient ofC11×Dic5×C13⋊C9, C3×C11×Dic5×C13⋊C3, C11×C13⋊C3×Dic15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 30);