Finite Group Databasebeta

← Prev (#46802015) Next (#46802017) →

C31×(C11⋊C5)⋊Dic5 #46802016

order34100
automorphism?
homologyAbelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(Dic5×C31)
unambiguous semidirect productDic55⋊(C5×C31)

Splittings

derivedC5×C11 ⋊ C4×C5×C31
HallC5×C31×C11⋊C5 ⋊ C4
HallC11×C31 ⋊ C5×Dic5
HallC5×C11⋊C5 ⋊ C4×C31
SylowC11 ⋊ C5×Dic5×C31

Subgroups

subgroupG/H
center, hypercenterC2×C31C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C4×C5×C31
FrattiniC2C31×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C11×C31C2×C5
prime radicalC2×C5×C31×C11⋊C5C2
cosocleC2×C5×C11C2×C5×C31
LCSG ▷ C5×C11
UCSC1 ◁ C2×C31

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

1550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 107);