Finite Group Databasebeta

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C3×C5×Dic143 #22575035

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic143

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ Dic13
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ C3×Dic13
HallC3×C13 ⋊ C5×Dic11
HallC3×C11 ⋊ C5×Dic13
SylowC13 ⋊ C3×C5×Dic11
SylowC11 ⋊ C3×C5×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D143
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC2C3×C5×D143
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×Dic143, C5×C11⋊(Dic13⋊C9), C3×C5×C11⋊(Dic13⋊C3), …
maximal normal subgroup ofC5×C9×Dic143, C5×C11⋊(Dic13⋊C9), C3×C5×C11⋊(Dic13⋊C3), …
maximal quotient ofC5×C9×Dic143, C3×C5×Dic429, C32×C5×Dic143

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 7);