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C11×#10587716 #20238795

order6006
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#10587716

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C11
HallC11×#63270 ⋊ C2
HallC7×C11×D13 ⋊ C3
HallC11×D13 ⋊ ΓL(1,𝔽8)
Hall#63270 ⋊ C2×C11
HallC7×D13 ⋊ C3×C11
HallC11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC7×C11 ⋊ D13⋊C3
HallD13 ⋊ C11×ΓL(1,𝔽8)
SylowC13 ⋊ C2×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#10587716
commutator, hypocenterC7×C13C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×#11763985, C11×#10587716⋊C2, C11⋊#11763985, …
maximal normal subgroup ofC11×#11763985, C11×#10587716⋊C2, C11⋊#11763985, …
maximal quotient ofC11×#11763957, C2×C11×#10587716, C11×#13109896, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6006, 23);