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C5×C11×C3⋊(C7⋊AGL(1,𝔽5)) #37528668

order23100
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C3⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C5×C11×C7⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C5×C11×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derivedC3×C5×C7 ⋊ C4×C5×C11
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ Dic21
HallC3×C7×C11 ⋊ C5×AGL(1,𝔽5)
HallC52×C7 ⋊ C11×Dic3
HallC7×C11 ⋊ C5×ΓL(1,𝔽16)
HallC3×C52 ⋊ C11×Dic7
HallC3×C11 ⋊ C5×C7⋊AGL(1,𝔽5)
SylowC52 ⋊ C11×Dic21
HallC3×C7 ⋊ C5×C11×AGL(1,𝔽5)
SylowC7 ⋊ C5×C11×ΓL(1,𝔽16)
SylowC3 ⋊ C5×C11×C7⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C7C4×C5×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleC3×C7×D5C2×C5×C11
LCSG ▷ C3×C5×C7
UCSC1 ◁ C5×C11

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) = 4620

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 479);