Finite Group Databasebeta

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C11×C49×Dic15 #44568314

order32340
automorphism?
homologyAbelianization (H1) = C4×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC11×C49×Dic15
unambiguous semidirect productC3⋊(C11×Dic5×C49)

Splittings

derived, HallC3×C5 ⋊ C4×C11×C49
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ Dic5
HallC3×C5×C49 ⋊ C4×C11
HallC5×C49 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C4×C49
HallC3×C49 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic3×C49
HallC3×C11 ⋊ Dic5×C49
SylowC5 ⋊ C11×Dic3×C49
SylowC3 ⋊ C11×Dic5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C11×C49D15
commutator, hypocenterC3×C5C4×C11×C49
FrattiniC2×C7C7×C11×D15
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11C2×C7
cosocleC2×C3×C5×C7C2×C7×C11
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

9702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 16);