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C11⋊C5×Dic39 #22575052

order8580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic39
unambiguous semidirect productC3⋊(Dic13×C11⋊C5)
unambiguous semidirect product(C11×Dic39)⋊C5

Splittings

derived, HallC3×C11×C13 ⋊ C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC11×Dic39 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic3
HallC3×C11⋊C5 ⋊ Dic13
HallC11×C13 ⋊ C5×Dic3
HallC3×C13 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×Dic13
SylowC13 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×Dic39
SylowC3 ⋊ Dic13×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D39
commutator, hypocenterC3×C11×C13C4×C5
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×Dic117, C11⋊C5×C3⋊(Dic13⋊C3), C3×C11⋊C5×Dic39, …
maximal normal subgroup ofC11⋊C5×C3⋊(Dic13⋊C3), C3×C11⋊C5×Dic39
maximal quotient ofC11⋊C5×Dic117, C3×C11⋊C5×Dic39, C11⋊C5×C3⋊Dic39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 24);