Finite Group Databasebeta

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C7×C3⋊(C7⋊#63118) #50304432

order38220
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derivedC3×C5×C7×C13 ⋊ C4×C7
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ #261
HallC72×C13 ⋊ Dic15
HallC5×C72 ⋊ C3⋊#261
HallC3×C5×C13 ⋊ C7×Dic7
HallC3×C72 ⋊ #63118
HallC5×C13 ⋊ C7×Dic21
SylowC72 ⋊ C3⋊#63118
HallC3×C13 ⋊ C7×Dic35
HallC3×C5 ⋊ C7×C7⋊#261
SylowC13 ⋊ C7×Dic105
SylowC5 ⋊ C7×C3⋊(C7⋊#261)
SylowC3 ⋊ C7×C7⋊#63118

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C7⋊#63118)
commutator, hypocenterC3×C5×C7×C13C4×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleC3×C5×C7×D13C2×C7
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C7

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

normal subgroups only

This group has 144 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

2961 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1118);