Finite Group Databasebeta

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C3×C29×C3⋊#1039 #39908011

order26100
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C5

Aliases

direct productC3×C29×C3⋊#1039
unambiguous semidirect productC3⋊(C3×C29×#1039)

Splittings

derivedC3×C52 ⋊ C3×C4×C29
HallC32×C52×C29 ⋊ C4
HallC52×C29 ⋊ C3×Dic3
HallC32×C29 ⋊ #1039
HallC32×C52 ⋊ C4×C29
SylowC52 ⋊ C3×Dic3×C29
SylowC32 ⋊ C29×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C3×C4×C29
FrattiniC2C3×C29×C3⋊(C5⋊D5)
Fitting, socle, prime radicalC2×C32×C52×C29C2
cosocleC2×C3×C52C2×C3×C29
LCSG ▷ C3×C52
UCSC1 ◁ C2×C3×C29

224 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, 245);