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C3×C4×C103⋊C3 #16814945

order3708
isoclinismisoclinic class of C103⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C103⋊C3
unambiguous semidirect product(C4×C103)⋊C32
unambiguous semidirect product(C3×C4×C103)⋊C3

Splittings

FittingC3×C4×C103 ⋊ C3
derived, SylowC103 ⋊ C32×C4
HallC4×C103 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C4C103⋊C3
commutator, hypocenterC103C32×C4
FrattiniC2C2×C3×C103⋊C3
FittingC3×C4×C103C3
socleC2×C3×C103C2×C3
prime radicalC2×C3×C103⋊C3C2
cosocleC2×C103C2×C32
LCSG ▷ C103
UCSC1 ◁ C3×C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1236

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×Dic5×C103⋊C3, C3×C4×C5×C103⋊C3, C3×AGL(1,𝔽5)×C103⋊C3, …
maximal normal subgroup ofC3×C4×C5×C103⋊C3, C3×C4×C7×C103⋊C3
maximal quotient ofC3×Dic5×C103⋊C3, C3×C4×C5×C103⋊C3, C3×AGL(1,𝔽5)×C103⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3708, 20);