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C11×(C11⋊C5)⋊Dic13 #44538109

order31460
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C11⋊C5)⋊Dic13
unambiguous semidirect product(C11⋊C5)⋊(C11×Dic13)
unambiguous semidirect productDic143⋊(C5×C11)

Splittings

derivedC11×C13 ⋊ C4×C5×C11
HallC11×C13×C11⋊C5 ⋊ C4
HallC11×Dic143 ⋊ C5
HallC112×C13 ⋊ C4×C5
HallC11×C11⋊C5 ⋊ Dic13
SylowC112 ⋊ C5×Dic13
SylowC13 ⋊ C11×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C11C13⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C4×C5×C11
FrattiniC2C11×C13⋊AGL(1,𝔽11)
Fitting, socleC2×C112×C13C2×C5
prime radicalC2×C11×C13×C11⋊C5C2
cosocleC2×C11×C13C2×C5×C11
LCSG ▷ C11×C13
UCSC1 ◁ C2×C11

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 49);