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C13×Dic221⋊C3 #46828174

order34476
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic221⋊C3
unambiguous semidirect productDic221⋊(C3×C13)

Splittings

derivedC13×C17 ⋊ C3×C4×C13
HallC13×Dic221 ⋊ C3
HallC13×C17×C13⋊C3 ⋊ C4
HallC132×C17 ⋊ C3×C4
HallC13×C13⋊C3 ⋊ Dic17
SylowC132 ⋊ C3×Dic17
SylowC17 ⋊ C13×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C13C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C3×C4×C13
FrattiniC2C13×C17⋊(D13⋊C3)
Fitting, socleC2×C132×C17C2×C3
prime radicalC2×C13×C17×C13⋊C3C2
cosocleC2×C13×C17C2×C3×C13
LCSG ▷ C13×C17
UCSC1 ◁ C2×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2652

Conjugacy classes & character table

1664 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 55);