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C4×C13×C109⋊C3 #30684246

order17004
isoclinismisoclinic class of C109⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×C109⋊C3
unambiguous semidirect product(C4×C109)⋊(C3×C13)

Splittings

Fitting, HallC4×C13×C109 ⋊ C3
derived, SylowC109 ⋊ C3×C4×C13
HallC13×C109 ⋊ C3×C4
HallC4×C109 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13C109⋊C3
commutator, hypocenterC109C3×C4×C13
FrattiniC2C2×C13×C109⋊C3
FittingC4×C13×C109C3
socleC2×C13×C109C2×C3
prime radicalC2×C13×C109⋊C3C2
cosocleC2×C109C2×C3×C13
LCSG ▷ C109
UCSC1 ◁ C4×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5668

Conjugacy classes & character table

2028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17004, 2);