Finite Group Databasebeta

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C22×C5×C11×C13⋊C3 #22575181

order8580
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C11×C13⋊C3

Splittings

Fitting, socle, HallC22×C5×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C5×C11
HallC5×C11×C13 ⋊ C22×C3
HallC22×C11×C13 ⋊ C3×C5
HallC22×C5×C13 ⋊ C3×C11
HallC11×C13 ⋊ C22×C3×C5
HallC5×C13 ⋊ C22×C3×C11
HallC22×C13 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC22×C5×C11C13⋊C3
commutator, hypocenterC13C22×C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C5×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×A4×C13⋊C3, C2×C5×D3×C11×C13⋊C3, C22×C3×C5×C11×C13⋊C3
maximal normal subgroup ofC5×C11×A4×C13⋊C3, C22×C3×C5×C11×C13⋊C3
maximal quotient ofC22×C5×C11×C13⋊C9, C2×C5×D3×C11×C13⋊C3, C22×C3×C5×C11×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 153);