Finite Group Databasebeta

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C5×Dic131⋊C13 #46801519

order34060
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic131⋊C13
unambiguous semidirect product(C5×Dic131)⋊C13

Splittings

derived, SylowC131 ⋊ C4×C5×C13
HallC5×C131⋊C13 ⋊ C4
HallC5×Dic131 ⋊ C13
HallC131⋊C13 ⋊ C4×C5
HallC5×C131 ⋊ C4×C13
HallDic131 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5D131⋊C13
commutator, hypocenterC131C4×C5×C13
FrattiniC2C5×D131⋊C13
Fitting, socleC2×C5×C131C2×C13
prime radicalC2×C5×C131⋊C13C2
cosocleC2×C131C2×C5×C13
LCSG ▷ C131
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34060, 12);