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C7×C13×ΓL(1,𝔽8)⋊Dic5 #50303609

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×ΓL(1,𝔽8)⋊Dic5
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×C13×Dic5)
unambiguous semidirect productDic35⋊(C3×C7×C13)

Splittings

derivedC5×C7 ⋊ C3×C4×C7×C13
HallC7×C13×Dic35 ⋊ C3
HallC5×C7×C13×ΓL(1,𝔽8) ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC7×C13×ΓL(1,𝔽8) ⋊ Dic5
HallC7×Dic35 ⋊ C3×C13
HallC5×C7×ΓL(1,𝔽8) ⋊ C4×C13
HallC72×C13 ⋊ C3×Dic5
HallC5×C72 ⋊ C3×C4×C13
HallC7×ΓL(1,𝔽8) ⋊ C13×Dic5
HallC5×C13 ⋊ C7×ΓL(1,𝔽8)⋊C4
SylowC72 ⋊ C3×C13×Dic5
SylowC5 ⋊ C7×C13×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C3×C4×C7×C13
FrattiniC2C7×C13×C5⋊AGL(1,𝔽7)
Fitting, socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C7×C13×ΓL(1,𝔽8)C2
cosocleC2×C5×C7C2×C3×C7×C13
LCSG ▷ C5×C7
UCSC1 ◁ C2×C7×C13

104 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

3094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 295);