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C11×ΓL(1,𝔽8)⋊C4 #11745101

order924
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C11)
unambiguous semidirect productDic7⋊(C3×C11)
unambiguous semidirect product(C11×Dic7)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C11
HallC11×Dic7 ⋊ C3
HallC11×ΓL(1,𝔽8) ⋊ C4
HallC7×C11 ⋊ C3×C4
HallDic7 ⋊ C3×C11
HallΓL(1,𝔽8) ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C11
FrattiniC2C11×AGL(1,𝔽7)
Fitting, socleC2×C7×C11C2×C3
prime radicalC2×C11×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C11
LCSG ▷ C7
UCSC1 ◁ C2×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 308

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×ΓL(1,𝔽8)⋊C4, (C11⋊AGL(1,𝔽7))⋊C4, #10597506⋊C3, …
maximal normal subgroup ofD11×ΓL(1,𝔽8)⋊C4, (C11⋊AGL(1,𝔽7))⋊C4, #10597506⋊C3, …
maximal quotient ofC11×ΓL(1,𝔽8)⋊C8, C2×C11×ΓL(1,𝔽8)⋊C4, C11×Dic7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(924, 2);