Finite Group Databasebeta

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C5×C3⋊#13097587 #37561124

order23940
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊#13097587
unambiguous semidirect productC3⋊(C5×#13097587)

Splittings

derivedC3×C7×C19 ⋊ C3×C4×C5
HallC3×C5×#87705 ⋊ C4
HallC3×#87705 ⋊ C4×C5
HallC5×C7×C19 ⋊ C3×Dic3
HallC7×C19 ⋊ C3×C5×Dic3
HallC5×C19 ⋊ C3⋊(ΓL(1,𝔽8)⋊C4)
HallC5×C7 ⋊ Dic3×C19⋊C3
SylowC19 ⋊ C5×C3⋊(ΓL(1,𝔽8)⋊C4)
SylowC7 ⋊ C5×Dic3×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊#11716326
commutator, hypocenterC3×C7×C19C3×C4×C5
FrattiniC2C5×C3⋊#11716326
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×#87705C2
cosocleC2×C3×C7×C19C2×C3×C5
LCSG ▷ C3×C7×C19
UCSC1 ◁ C2×C5

112 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 7980

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 256);