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C22×C11×C31⋊C25 #46801972

order34100
automorphism?
homologyAbelianization (H1) = C22×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×C31⋊C25
unambiguous semidirect product(C22×C31)⋊(C11×C25)

Splittings

derived, SylowC31 ⋊ C22×C11×C25
HallC22×C11×C31 ⋊ C25
HallC11×C31 ⋊ C22×C25
HallC22×C31 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11ΓL(1,𝔽32)
commutator, hypocenterC31C22×C11×C25
FrattiniC5C22×C11×ΓL(1,𝔽32)
Fitting, socle, prime radicalC22×C5×C11×C31C5
cosocleC5×C31C22×C5×C11
LCSG ▷ C31
UCSC1 ◁ C22×C5×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34100

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 63);