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C5×C13×C3⋊(C7⋊AGL(1,𝔽5)) #41031997

order27300
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C3⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C5×C13×C7⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C5×C13×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C4
derivedC3×C5×C7 ⋊ C4×C5×C13
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ Dic7
HallC3×C52×C7 ⋊ C4×C13
HallC52×C13 ⋊ Dic21
HallC3×C7×C13 ⋊ C5×AGL(1,𝔽5)
HallC52×C7 ⋊ Dic3×C13
HallC7×C13 ⋊ C5×ΓL(1,𝔽16)
HallC3×C52 ⋊ C13×Dic7
HallC3×C13 ⋊ C5×C7⋊AGL(1,𝔽5)
SylowC52 ⋊ C13×Dic21
HallC3×C7 ⋊ C5×C13×AGL(1,𝔽5)
SylowC7 ⋊ C5×C13×ΓL(1,𝔽16)
SylowC3 ⋊ C5×C13×C7⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5×C13C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C4×C5×C13
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C5×C7×D5×C13C2
cosocleC3×C7×D5C2×C5×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C13

104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 52 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

2925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 887);