Finite Group Databasebeta

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C11×Dic5×ΓL(1,𝔽32) #46802015

order34100
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic5×ΓL(1,𝔽32)
unambiguous semidirect product(Dic5×C31)⋊(C5×C11)

Splittings

derivedC5×C31 ⋊ C4×C5×C11
HallC5×C11×ΓL(1,𝔽32) ⋊ C4
HallC5×ΓL(1,𝔽32) ⋊ C4×C11
HallC11×C31 ⋊ C5×Dic5
SylowC31 ⋊ C5×C11×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C11D5×ΓL(1,𝔽32)
commutator, hypocenterC5×C31C4×C5×C11
FrattiniC2D5×C11×ΓL(1,𝔽32)
Fitting, socleC2×C5×C11×C31C2×C5
prime radicalC2×C5×C11×ΓL(1,𝔽32)C2
cosocleC2×C5×C31C2×C5×C11
LCSG ▷ C5×C31
UCSC1 ◁ C2×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 106);