Finite Group Databasebeta

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C5×Dic693 #28357348

order13860
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic693
unambiguous semidirect productC7⋊(C5×Dic99)
unambiguous semidirect productC9⋊(C5×Dic77)

Splittings

derived, HallC7×C9×C11 ⋊ C4×C5
HallC5×C7×C9×C11 ⋊ C4
HallC5×C9×C11 ⋊ Dic7
HallC5×C7×C11 ⋊ Dic9
HallC5×C7×C9 ⋊ Dic11
HallC9×C11 ⋊ C5×Dic7
HallC7×C11 ⋊ C5×Dic9
HallC7×C9 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic63
HallC5×C9 ⋊ Dic77
HallC5×C7 ⋊ Dic99
SylowC11 ⋊ C5×Dic63
SylowC9 ⋊ C5×Dic77
SylowC7 ⋊ C5×Dic99

Subgroups

subgroupG/H
center, hypercenterC2×C5D693
commutator, hypocenterC7×C9×C11C4×C5
FrattiniC2×C3C5×D231
FittingC2×C5×C7×C9×C11C2
socle, prime radicalC2×C3×C5×C7×C11D3
cosocleC2×C7×C9×C11C2×C5
LCSG ▷ C7×C9×C11
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13860

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 15);