Finite Group Databasebeta

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C3×C5×Dic3×C149 #41001259

order26820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C149 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C149
unambiguous semidirect productC3⋊(C3×C4×C5×C149)

Splittings

derivedC3 ⋊ C3×C4×C5×C149
HallC32×C5×C149 ⋊ C4
HallC32×C149 ⋊ C4×C5
HallC32×C5 ⋊ C4×C149
SylowC32 ⋊ C4×C5×C149

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C149D3
commutator, hypocenterC3C3×C4×C5×C149
FrattiniC2C3×C5×D3×C149
Fitting, socle, prime radicalC2×C32×C5×C149C2
cosocleC2×C3C2×C3×C5×C149
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C149

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8940

Conjugacy classes & character table

13410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 45);