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C4×C11×C31⋊C25 #46801911

order34100
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×C31⋊C25
unambiguous semidirect product(C4×C31)⋊(C11×C25)

Splittings

derived, SylowC31 ⋊ C4×C11×C25
HallC4×C11×C31 ⋊ C25
HallC11×C31 ⋊ C4×C25
HallC4×C31 ⋊ C11×C25

Subgroups

subgroupG/H
center, hypercenterC4×C5×C11ΓL(1,𝔽32)
commutator, hypocenterC31C4×C11×C25
FrattiniC2×C5C2×C11×ΓL(1,𝔽32)
FittingC4×C5×C11×C31C5
socle, prime radicalC2×C5×C11×C31C2×C5
cosocleC2×C5×C31C2×C5×C11
LCSG ▷ C31
UCSC1 ◁ C4×C5×C11

36 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, 2);