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C22×C11×C13⋊C9 #19104155

order5148
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×C13⋊C9

Splittings

derived, SylowC13 ⋊ C22×C9×C11
HallC22×C11×C13 ⋊ C9
HallC11×C13 ⋊ C22×C9
HallC22×C13 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC22×C3×C11C13⋊C3
commutator, hypocenterC13C22×C9×C11
FrattiniC3C22×C11×C13⋊C3
Fitting, socleC22×C3×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C11⋊C5×C13⋊C9, C2×D5×C11×C13⋊C9, C22×C5×C11×C13⋊C9, …
maximal normal subgroup ofC22×C11⋊C5×C13⋊C9, C22×C5×C11×C13⋊C9, C22×C7×C11×C13⋊C9
maximal quotient ofC2×D5×C11×C13⋊C9, C22×C5×C11×C13⋊C9, C2×C11×#13109900, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 31);