Finite Group Databasebeta

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C5×Dic1305 #39907830

order26100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1305
unambiguous semidirect productC9⋊(C5×Dic145)

Splittings

derivedC5×C9×C29 ⋊ C4×C5
HallC52×C9×C29 ⋊ C4
HallC52×C29 ⋊ Dic9
HallC9×C29 ⋊ C5×Dic5
HallC52×C9 ⋊ Dic29
SylowC29 ⋊ C5×Dic45
SylowC52 ⋊ Dic261
SylowC9 ⋊ C5×Dic145

Subgroups

subgroupG/H
center, hypercenterC2×C5D1305
commutator, hypocenterC5×C9×C29C4×C5
FrattiniC2×C3C5×D435
FittingC2×C52×C9×C29C2
socle, prime radicalC2×C3×C52×C29D3
cosocleC2×C5×C9×C29C2×C5
LCSG ▷ C5×C9×C29
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

6540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 64);