Finite Group Databasebeta

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C3×C29×Dic75 #39907809

order26100
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×Dic75
unambiguous semidirect productC3⋊(C3×C29×Dic25)

Splittings

derivedC3×C25 ⋊ C3×C4×C29
HallC32×C25×C29 ⋊ C4
HallC25×C29 ⋊ C3×Dic3
HallC32×C29 ⋊ Dic25
HallC32×C25 ⋊ C4×C29
SylowC25 ⋊ C3×Dic3×C29
SylowC32 ⋊ C29×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D75
commutator, hypocenterC3×C25C3×C4×C29
FrattiniC2×C5C3×C29×D15
FittingC2×C32×C25×C29C2
socle, prime radicalC2×C32×C5×C29D5
cosocleC2×C3×C25C2×C3×C29
LCSG ▷ C3×C25
UCSC1 ◁ C2×C3×C29

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8700

Conjugacy classes & character table

6786 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 43);