Finite Group Databasebeta

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C5×Dic429 #22575043

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

Aliases

direct productC5×Dic429
unambiguous semidirect productC3⋊(C5×Dic143)

Splittings

derived, HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ Dic3
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ Dic13
HallC11×C13 ⋊ C5×Dic3
HallC5×C13 ⋊ Dic33
HallC5×C11 ⋊ Dic39
HallC3×C13 ⋊ C5×Dic11
HallC3×C11 ⋊ C5×Dic13
HallC3×C5 ⋊ Dic143
SylowC13 ⋊ C5×Dic33
SylowC11 ⋊ C5×Dic39
SylowC3 ⋊ C5×Dic143

Subgroups

subgroupG/H
center, hypercenterC2×C5D429
commutator, hypocenterC3×C11×C13C4×C5
FrattiniC2C5×D429
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×Dic1287, C5×C3⋊(C11⋊(Dic13⋊C3)), C5×C3⋊Dic429, …
maximal normal subgroup ofC5×C3⋊(C11⋊(Dic13⋊C3)), C3×C5×Dic429
maximal quotient ofC5×Dic1287, C5×C3⋊Dic429, C3×C5×Dic429

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 15);