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C3×C11×AGL(1,𝔽5)×C49 #44568377

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×AGL(1,𝔽5)×C49

Splittings

Fitting, HallC3×C5×C11×C49 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C11×C49
HallC5×C11×C49 ⋊ C3×C4
HallC3×C5×C49 ⋊ C4×C11
HallC5×C49 ⋊ C3×C4×C11
HallC3×C5×C11 ⋊ C4×C49
HallC5×C11 ⋊ C3×C4×C49
HallC3×C5 ⋊ C4×C11×C49

Subgroups

subgroupG/H
center, hypercenterC3×C11×C49AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C11×C49
FrattiniC7C3×C7×C11×AGL(1,𝔽5)
FittingC3×C5×C11×C49C4
socleC3×C5×C7×C11C4×C7
prime radicalC3×C7×D5×C11C2×C7
cosocleC7×D5C2×C3×C7×C11
LCSG ▷ C5
UCSC1 ◁ C3×C11×C49

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

8085 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 79);