Finite Group Databasebeta

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C3×Dic715 #22575039

order8580
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic715
unambiguous semidirect productC11⋊(C3×Dic65)

Splittings

derived, HallC5×C11×C13 ⋊ C3×C4
HallC3×C5×C11×C13 ⋊ C4
HallC3×C11×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C3×Dic5
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ C3×Dic13
HallC3×C13 ⋊ Dic55
HallC3×C11 ⋊ Dic65
HallC3×C5 ⋊ Dic143
SylowC13 ⋊ C3×Dic55
SylowC11 ⋊ C3×Dic65
SylowC5 ⋊ C3×Dic143

Subgroups

subgroupG/H
center, hypercenterC2×C3D715
commutator, hypocenterC5×C11×C13C3×C4
FrattiniC2C3×D715
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2154 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×Dic715, C11⋊(Dic65⋊C9), C3×C11⋊(Dic65⋊C3), …
maximal normal subgroup ofC9×Dic715, C11⋊(Dic65⋊C9), C3×C11⋊(Dic65⋊C3), …
maximal quotient ofC9×Dic715, C3×Dic2145, C32×Dic715

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 11);