Finite Group Databasebeta

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C2×C3×C5×C13×D11 #22575195

order8580
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C13×D11

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2
derived, SylowC11 ⋊ C22×C3×C5×C13
HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C22×C5
HallC3×C5×C11 ⋊ C22×C13
HallC11×C13 ⋊ C22×C3×C5
HallC5×C11 ⋊ C22×C3×C13
HallC3×C11 ⋊ C22×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C13D11
commutator, hypocenterC11C22×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C11
UCSC1 ◁ C2×C3×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D11×C13⋊C9, C2×C5×C9×C13×D11, C2×C3×C5×D11×C13⋊C3, …
maximal normal subgroup ofC2×C5×D11×C13⋊C9, C2×C5×C9×C13×D11, C2×C3×C5×D11×C13⋊C3, …
maximal quotient ofC2×C5×C9×C13×D11, C3×C5×D3×C13×D11, C2×C32×C5×C13×D11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 167);