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C13×(C11⋊C5)⋊Dic11 #44538125

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

Aliases

direct productC13×(C11⋊C5)⋊Dic11
unambiguous semidirect product(C11⋊C5)⋊(C13×Dic11)

Splittings

derived, SylowC112 ⋊ C4×C5×C13
HallC11×C13×C11⋊C5 ⋊ C4
HallC13×C11⋊Dic11 ⋊ C5
HallC112×C13 ⋊ C4×C5
HallC11×C11⋊C5 ⋊ C4×C13
HallC11⋊Dic11 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13(C11⋊C5)⋊D11
commutator, hypocenterC112C4×C5×C13
FrattiniC2C13×(C11⋊C5)⋊D11
Fitting, socleC2×C112×C13C2×C5
prime radicalC2×C11×C13×C11⋊C5C2
cosocleC2×C112C2×C5×C13
LCSG ▷ C112
UCSC1 ◁ C2×C13

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 65);