Finite Group Databasebeta

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C5×C11×Dic3×C13 #22575040

order8580
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic3×C13
unambiguous semidirect productC3⋊(C4×C5×C11×C13)

Splittings

derived, SylowC3 ⋊ C4×C5×C11×C13
HallC3×C5×C11×C13 ⋊ C4
HallC3×C11×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C13
HallC3×C13 ⋊ C4×C5×C11
HallC3×C11 ⋊ C4×C5×C13
HallC3×C5 ⋊ C4×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C13D3
commutator, hypocenterC3C4×C5×C11×C13
FrattiniC2C5×D3×C11×C13
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C3
UCSC1 ◁ C2×C5×C11×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4290 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×C13×Dic9, C5×C11×Dic3×C13⋊C3, C5×C11×C13×C3⋊Dic3, …
maximal normal subgroup ofC5×C11×Dic3×C13⋊C3, C3×C5×C11×Dic3×C13
maximal quotient ofC5×C11×C13×Dic9, C5×C11×C13×C3⋊Dic3, C3×C5×C11×Dic3×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 12);