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C13×Dic131⋊C5 #46801522

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

Aliases

direct productC13×Dic131⋊C5
unambiguous semidirect product(C13×Dic131)⋊C5

Splittings

derived, SylowC131 ⋊ C4×C5×C13
HallC13×C131⋊C5 ⋊ C4
HallC13×Dic131 ⋊ C5
HallC13×C131 ⋊ C4×C5
HallC131⋊C5 ⋊ C4×C13
HallDic131 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D131⋊C5
commutator, hypocenterC131C4×C5×C13
FrattiniC2C13×D131⋊C5
Fitting, socleC2×C13×C131C2×C5
prime radicalC2×C13×C131⋊C5C2
cosocleC2×C131C2×C5×C13
LCSG ▷ C131
UCSC1 ◁ C2×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6812

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34060, 15);