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Dic3×C41×C49 #37563002

order24108
automorphism?
homologyAbelianization (H1) = C4×C41×C49 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C41×C49
unambiguous semidirect productC3⋊(C4×C41×C49)

Splittings

derived, SylowC3 ⋊ C4×C41×C49
HallC3×C41×C49 ⋊ C4
HallC3×C49 ⋊ C4×C41
HallC3×C41 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC2×C41×C49D3
commutator, hypocenterC3C4×C41×C49
FrattiniC2×C7D3×C7×C41
FittingC2×C3×C41×C49C2
socle, prime radicalC2×C3×C7×C41C2×C7
cosocleC2×C3×C7C2×C7×C41
LCSG ▷ C3
UCSC1 ◁ C2×C41×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24108

Conjugacy classes & character table

12054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24108, 9);