Finite Group Databasebeta

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C11⋊C5×Dic147 #44568323

order32340
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×Dic147
unambiguous semidirect productC3⋊(C11⋊C5×Dic49)
unambiguous semidirect productC49⋊(Dic3×C11⋊C5)
unambiguous semidirect product(C11×Dic147)⋊C5

Splittings

derived, HallC3×C11×C49 ⋊ C4×C5
HallC3×C49×C11⋊C5 ⋊ C4
HallC11×Dic147 ⋊ C5
HallC49×C11⋊C5 ⋊ Dic3
HallC11×C49 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic49
HallC3×C49 ⋊ C4×C11⋊C5
SylowC49 ⋊ Dic3×C11⋊C5
HallC3×C11 ⋊ C5×Dic49
SylowC11 ⋊ C5×Dic147
SylowC3 ⋊ C11⋊C5×Dic49

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D147
commutator, hypocenterC3×C11×C49C4×C5
FrattiniC2×C7D21×C11⋊C5
Fitting, cosocleC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C5×D7
prime radicalC2×C3×C7×C11⋊C5D7
LCSG ▷ C3×C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 25);