Finite Group Databasebeta

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C11×C31×#1035 #46801974

order34100
automorphism?
homologyAbelianization (H1) = C4×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC11×C31×#1035

Splittings

Fitting, HallC11×C25×C31 ⋊ C4
derived, SylowC25 ⋊ C4×C11×C31
HallC25×C31 ⋊ C4×C11
HallC11×C25 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC11×C31#1035
commutator, hypocenterC25C4×C11×C31
FrattiniC5C11×AGL(1,𝔽5)×C31
FittingC11×C25×C31C4
socleC5×C11×C31AGL(1,𝔽5)
prime radicalC11×C31×D25C2
cosocleD25C2×C11×C31
LCSG ▷ C25
UCSC1 ◁ C11×C31

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8525

Conjugacy classes & character table

3410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 65);