Finite Group Databasebeta

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C5×C13×Dic33 #22575042

order8580
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic33
unambiguous semidirect productC3⋊(C5×C13×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C5×C13
HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ C4×C13
HallC11×C13 ⋊ C5×Dic3
HallC5×C11 ⋊ Dic3×C13
HallC3×C13 ⋊ C5×Dic11
HallC3×C5 ⋊ C13×Dic11
SylowC11 ⋊ C5×Dic3×C13
SylowC3 ⋊ C5×C13×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D33
commutator, hypocenterC3×C11C4×C5×C13
FrattiniC2C5×C13×D33
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13×Dic99, C5×C13⋊C3×Dic33, C5×C13×C3⋊Dic33, …
maximal normal subgroup ofC5×C13⋊C3×Dic33, C3×C5×C13×Dic33
maximal quotient ofC5×C13×Dic99, C5×C13×C3⋊Dic33, C3×C5×C13×Dic33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 14);