Finite Group Databasebeta

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C11×Dic735 #44568316

order32340
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic735
unambiguous semidirect productC3⋊(C11×Dic245)
unambiguous semidirect productC49⋊(C11×Dic15)

Splittings

derived, HallC3×C5×C49 ⋊ C4×C11
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ Dic5
HallC11×C49 ⋊ Dic15
HallC5×C49 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic147
SylowC49 ⋊ C11×Dic15
HallC3×C11 ⋊ Dic245
HallC3×C5 ⋊ C11×Dic49
SylowC5 ⋊ C11×Dic147
SylowC3 ⋊ C11×Dic245

Subgroups

subgroupG/H
center, hypercenterC2×C11D735
commutator, hypocenterC3×C5×C49C4×C11
FrattiniC2×C7C11×D105
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11D7
cosocleC2×C3×C5×C49C2×C11
LCSG ▷ C3×C5×C49
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 18);