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C13×ΓL(1,𝔽8)×Dic11 #26046436

order12012
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×Dic11
unambiguous semidirect productC11⋊(C4×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic11)⋊(C3×C13)

Splittings

derived, HallC7×C11 ⋊ C3×C4×C13
HallC7×C13×Dic11 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C13 ⋊ C3×C4
HallC7×Dic11 ⋊ C3×C13
HallC11×ΓL(1,𝔽8) ⋊ C4×C13
HallC11×C13 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×Dic11
SylowC11 ⋊ C4×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C3×C4×C13
FrattiniC2C13×ΓL(1,𝔽8)×D11
Fitting, socleC2×C7×C11×C13C2×C3
prime radicalC2×C11×C13×ΓL(1,𝔽8)C2
cosocleC2×C7×C11C2×C3×C13
LCSG ▷ C7×C11
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

910 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×C13×ΓL(1,𝔽8)×Dic11, C13×ΓL(1,𝔽8)×Dic33
maximal normal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×C13×ΓL(1,𝔽8)×Dic11
maximal quotient ofC13×Dic11×C7⋊C9, C3×C13×ΓL(1,𝔽8)×Dic11, C13×ΓL(1,𝔽8)×Dic33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 26);