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ΓL(1,𝔽8)×Dic143 #26046440

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

Aliases

direct productΓL(1,𝔽8)×Dic143
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×Dic13)

Splittings

derived, HallC7×C11×C13 ⋊ C3×C4
HallC7×Dic143 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C4
HallC13×ΓL(1,𝔽8) ⋊ Dic11
HallC11×ΓL(1,𝔽8) ⋊ Dic13
HallC11×C13 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×Dic13
SylowC13 ⋊ ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ ΓL(1,𝔽8)×Dic13
SylowC7 ⋊ C3×Dic143

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D143
commutator, hypocenterC7×C11×C13C3×C4
Fitting, socle, cosocleC2×C7×C11×C13C2×C3
prime radicalC2×C11×C13×ΓL(1,𝔽8)C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

730 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×C11⋊(Dic13⋊C3), C3×ΓL(1,𝔽8)×Dic143, ΓL(1,𝔽8)×Dic429
maximal normal subgroup ofΓL(1,𝔽8)×C11⋊(Dic13⋊C3), C3×ΓL(1,𝔽8)×Dic143
maximal quotient ofC7⋊C9×Dic143, C3×ΓL(1,𝔽8)×Dic143, ΓL(1,𝔽8)×Dic429

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 30);