Finite Group Databasebeta

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C49×Dic165 #44568315

order32340
automorphism?
homologyAbelianization (H1) = C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC49×Dic165
unambiguous semidirect productC3⋊(C49×Dic55)
unambiguous semidirect productC11⋊(C49×Dic15)

Splittings

derived, HallC3×C5×C11 ⋊ C4×C49
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ Dic5
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ Dic15
HallC5×C49 ⋊ Dic33
HallC3×C49 ⋊ Dic55
HallC5×C11 ⋊ Dic3×C49
HallC3×C11 ⋊ Dic5×C49
HallC3×C5 ⋊ Dic11×C49
SylowC11 ⋊ C49×Dic15
SylowC5 ⋊ C49×Dic33
SylowC3 ⋊ C49×Dic55

Subgroups

subgroupG/H
center, hypercenterC2×C49D165
commutator, hypocenterC3×C5×C11C4×C49
FrattiniC2×C7C7×D165
FittingC2×C3×C5×C11×C49C2
socle, prime radical, cosocleC2×C3×C5×C7×C11C2×C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 17);