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C11×#11763964 #26046450

order12012
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#11763964

Splittings

derived, HallC7×C13 ⋊ C3×C4×C11
HallC11×Dic91 ⋊ C3
HallC11×#63271 ⋊ C4
HallC7×C11×C13 ⋊ C3×C4
HallDic91 ⋊ C3×C11
Hall#63271 ⋊ C4×C11
HallC11×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C11 ⋊ Dic13⋊C3
SylowC13 ⋊ C11×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C11×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#10587723
commutator, hypocenterC7×C13C3×C4×C11
FrattiniC2C11×#10587723
Fitting, socleC2×C7×C11×C13C2×C3
prime radicalC2×C11×#63271C2
cosocleC2×C7×C13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

462 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊(Dic13⋊C3), C3×C11×#11763964, C11×C3⋊#11763964
maximal normal subgroup ofC11×ΓL(1,𝔽8)⋊(Dic13⋊C3), C3×C11×#11763964
maximal quotient ofC11×#15692572, C3×C11×#11763964, C11×C3⋊#11763964

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 40);