Finite Group Databasebeta

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C32×C5×D341 #44501869

order30690
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D341

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derived, HallC11×C31 ⋊ C2×C32×C5
HallC32×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ C2×C32
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ D31
HallC32×C31 ⋊ C5×D11
HallC5×C31 ⋊ C32×D11
HallC32×C11 ⋊ C5×D31
HallC5×C11 ⋊ C32×D31
SylowC31 ⋊ C32×C5×D11
SylowC11 ⋊ C32×C5×D31

Subgroups

subgroupG/H
center, hypercenterC32×C5D341
commutator, cosocle, hypocenterC11×C31C2×C32×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C11×C31
UCSC1 ◁ C32×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 236);