Finite Group Databasebeta

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C5×C3⋊(C7⋊#63118) #41031971

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

Aliases

direct productC5×C3⋊(C7⋊#63118)
unambiguous semidirect productC3⋊(C5×C7⋊#63118)
unambiguous semidirect productC7⋊(C5×C3⋊#63118)

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C4
derivedC3×C5×C7×C13 ⋊ C4×C5
HallC52×C7×C13 ⋊ Dic3
HallC3×C52×C13 ⋊ Dic7
HallC3×C52×C7 ⋊ #261
HallC52×C13 ⋊ Dic21
HallC3×C7×C13 ⋊ C5×Dic5
HallC52×C7 ⋊ C3⋊#261
HallC7×C13 ⋊ C5×Dic15
HallC3×C52 ⋊ C7⋊#261
HallC3×C13 ⋊ C5×Dic35
SylowC52 ⋊ C3⋊(C7⋊#261)
HallC3×C7 ⋊ C5×#63118
SylowC13 ⋊ C5×Dic105
SylowC7 ⋊ C5×C3⋊#63118
SylowC3 ⋊ C5×C7⋊#63118

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C7⋊#63118)
commutator, hypocenterC3×C5×C7×C13C4×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C13C4
prime radicalC3×C52×C7×D13C2
cosocleC3×C5×C7×D13C2×C5
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C5

128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 2730

Conjugacy classes & character table

2115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 861);