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C11×C13×Dic11⋊C5 #44538108

order31460
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C11×C13)
unambiguous semidirect product(C11⋊C5)⋊(C4×C11×C13)
unambiguous semidirect product(C13×Dic11)⋊(C5×C11)

Splittings

derivedC11 ⋊ C4×C5×C11×C13
HallC11×C13×C11⋊C5 ⋊ C4
HallC11×C13×Dic11 ⋊ C5
HallC112×C13 ⋊ C4×C5
HallC11×C11⋊C5 ⋊ C4×C13
HallC11×Dic11 ⋊ C5×C13
SylowC112 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C11×C13
FrattiniC2C11×C13×AGL(1,𝔽11)
Fitting, socleC2×C112×C13C2×C5
prime radicalC2×C11×C13×C11⋊C5C2
cosocleC2×C11C2×C5×C11×C13
LCSG ▷ C11
UCSC1 ◁ C2×C11×C13

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

3146 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 48);