Finite Group Databasebeta

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C3×C49×Dic55 #44568307

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×Dic55
unambiguous semidirect productC11⋊(C3×Dic5×C49)

Splittings

derived, HallC5×C11 ⋊ C3×C4×C49
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ C3×C4
HallC3×C11×C49 ⋊ Dic5
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ C3×Dic5
HallC5×C49 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C4×C49
HallC3×C11 ⋊ Dic5×C49
HallC3×C5 ⋊ Dic11×C49
SylowC11 ⋊ C3×Dic5×C49
SylowC5 ⋊ C3×Dic11×C49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C49D55
commutator, hypocenterC5×C11C3×C4×C49
FrattiniC2×C7C3×C7×D55
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11C2×C7
cosocleC2×C5×C7×C11C2×C3×C7
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 9);