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C3×Dic3×C841 #44475552

order30276
automorphism?
homologyAbelianization (H1) = C3×C4×C841 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C841
unambiguous semidirect productC3⋊(C3×C4×C841)

Splittings

derivedC3 ⋊ C3×C4×C841
HallC32×C841 ⋊ C4
SylowC32 ⋊ C4×C841

Subgroups

subgroupG/H
center, hypercenterC2×C3×C841D3
commutator, hypocenterC3C3×C4×C841
FrattiniC2×C29C3×D3×C29
FittingC2×C32×C841C2
socle, prime radicalC2×C32×C29C2×C29
cosocleC2×C3×C29C2×C3×C29
LCSG ▷ C3
UCSC1 ◁ C2×C3×C841

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10092

Conjugacy classes & character table

15138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30276, 15);