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C4×C13×#10597244 #44538136

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

Aliases

direct productC4×C13×#10597244

Splittings

Fitting, HallC4×C112×C13 ⋊ C5
derived, SylowC112 ⋊ C4×C5×C13
HallC112×C13 ⋊ C4×C5
HallC4×C112 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13#10597244
commutator, hypocenterC112C4×C5×C13
FrattiniC2C2×C13×#10597244
FittingC4×C112×C13C5
socleC2×C112×C13C2×C5
prime radicalC2×C13×#10597244C2
cosocleC2×C112C2×C5×C13
LCSG ▷ C112
UCSC1 ◁ C4×C13

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

1508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 76);