Finite Group Databasebeta

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C5×C29×C3⋊Dic15 #39908007

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

Aliases

direct productC5×C29×C3⋊Dic15
unambiguous semidirect productC3⋊(C5×C29×Dic15)

Splittings

derivedC32×C5 ⋊ C4×C5×C29
HallC32×C52×C29 ⋊ C4
HallC52×C29 ⋊ C3⋊Dic3
HallC32×C29 ⋊ C5×Dic5
HallC32×C52 ⋊ C4×C29
SylowC52 ⋊ C29×C3⋊Dic3
SylowC32 ⋊ C5×Dic5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29C3⋊D15
commutator, hypocenterC32×C5C4×C5×C29
FrattiniC2C5×C29×C3⋊D15
Fitting, socle, prime radicalC2×C32×C52×C29C2
cosocleC2×C32×C5C2×C5×C29
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5×C29

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

6960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 241);