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ΓL(1,𝔽8)⋊C4×C103 #22575745

order8652
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C103 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C103
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C103)
unambiguous semidirect productDic7⋊(C3×C103)

Splittings

derived, SylowC7 ⋊ C3×C4×C103
HallDic7×C103 ⋊ C3
HallΓL(1,𝔽8)×C103 ⋊ C4
HallC7×C103 ⋊ C3×C4
HallDic7 ⋊ C3×C103
HallΓL(1,𝔽8) ⋊ C4×C103

Subgroups

subgroupG/H
center, hypercenterC2×C103AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C103
FrattiniC2AGL(1,𝔽7)×C103
Fitting, socleC2×C7×C103C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C103

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1442 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊C4×C103⋊C3, C3×ΓL(1,𝔽8)⋊C4×C103, C103×C3⋊(ΓL(1,𝔽8)⋊C4)
maximal normal subgroup ofΓL(1,𝔽8)⋊C4×C103⋊C3, C3×ΓL(1,𝔽8)⋊C4×C103
maximal quotient ofC103×Dic7⋊C9, C3×ΓL(1,𝔽8)⋊C4×C103, C103×C3⋊(ΓL(1,𝔽8)⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 18);