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C13×ΓL(1,𝔽8)×Dic15 #30655248

order16380
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×Dic15
unambiguous semidirect productC3⋊(C13×Dic5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic15)⋊(C3×C13)

Splittings

derivedC3×C5×C7 ⋊ C3×C4×C13
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C4
HallC3×C13×ΓL(1,𝔽8) ⋊ Dic5
HallC5×C7×C13 ⋊ C3×Dic3
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C13
HallC7×C13 ⋊ C3×Dic15
HallC5×C13 ⋊ Dic3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ C13×Dic5
HallC5×C7 ⋊ C3×Dic3×C13
SylowC7 ⋊ C3×C13×Dic15
SylowC5 ⋊ Dic3×C13×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)×D15
commutator, hypocenterC3×C5×C7C3×C4×C13
FrattiniC2C13×ΓL(1,𝔽8)×D15
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C13×ΓL(1,𝔽8)C2
cosocleC2×C3×C5×C7C2×C3×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C13

112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 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

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 298);