Finite Group Databasebeta

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C2×C3×D5×C11×C13 #22575193

order8580
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D5×C11×C13
unambiguous semidirect productC5⋊(C22×C3×C11×C13)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C11×C13)

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C11×C13
HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C22×C3
HallC3×C5×C13 ⋊ C22×C11
HallC3×C5×C11 ⋊ C22×C13
HallC5×C13 ⋊ C22×C3×C11
HallC5×C11 ⋊ C22×C3×C13
HallC3×C5 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C13D5
commutator, hypocenterC5C22×C3×C11×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C11×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D5×C11×C13⋊C9, C2×C9×D5×C11×C13, C2×C3×D5×C11×C13⋊C3, …
maximal normal subgroup ofC2×D5×C11×C13⋊C9, C2×C9×D5×C11×C13, C2×C3×D5×C11×C13⋊C3, …
maximal quotient ofC2×C9×D5×C11×C13, C3×D3×D5×C11×C13, C2×C32×D5×C11×C13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 165);