Finite Group Databasebeta

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C5×Dic855 #30685453

order17100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic855
unambiguous semidirect productC9⋊(C5×Dic95)
unambiguous semidirect productC19⋊(C5×Dic45)

Splittings

derivedC5×C9×C19 ⋊ C4×C5
HallC52×C9×C19 ⋊ C4
HallC52×C19 ⋊ Dic9
HallC52×C9 ⋊ Dic19
HallC9×C19 ⋊ C5×Dic5
SylowC52 ⋊ Dic171
SylowC19 ⋊ C5×Dic45
SylowC9 ⋊ C5×Dic95

Subgroups

subgroupG/H
center, hypercenterC2×C5D855
commutator, hypocenterC5×C9×C19C4×C5
FrattiniC2×C3C5×D285
FittingC2×C52×C9×C19C2
socle, prime radicalC2×C3×C52×C19D3
cosocleC2×C5×C9×C19C2×C5
LCSG ▷ C5×C9×C19
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3420

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 90);