Finite Group Databasebeta

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C32×C25×D77 #46831433

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C25 · Schur multiplier (H2) = C3

Aliases

direct productC32×C25×D77

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC7×C11 ⋊ C2×C32×C25
HallC32×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ C2×C32
HallC32×C7×C25 ⋊ D11
HallC32×C7×C11 ⋊ C2×C25
HallC11×C25 ⋊ C32×D7
HallC7×C25 ⋊ C32×D11
HallC32×C11 ⋊ D7×C25
HallC32×C7 ⋊ D11×C25
SylowC11 ⋊ C32×D7×C25
SylowC7 ⋊ C32×D11×C25

Subgroups

subgroupG/H
center, hypercenterC32×C25D77
commutator, hypocenterC7×C11C2×C32×C25
FrattiniC5C32×C5×D77
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11C2×C5
prime radicalC32×C5×D77C5
cosocleC5×C7×C11C2×C32×C5
LCSG ▷ C7×C11
UCSC1 ◁ C32×C25

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

9000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 76);