Finite Group Databasebeta

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C7×C13×Dic105 #50303683

order38220
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×Dic105
unambiguous semidirect productC3⋊(C7×C13×Dic35)
unambiguous semidirect productC7⋊(C7×C13×Dic15)

Splittings

derivedC3×C5×C7 ⋊ C4×C7×C13
HallC3×C5×C72×C13 ⋊ C4
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ C4×C13
HallC72×C13 ⋊ Dic15
HallC5×C72 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ C7×Dic7
HallC3×C72 ⋊ C13×Dic5
HallC5×C13 ⋊ C7×Dic21
SylowC72 ⋊ C13×Dic15
HallC3×C13 ⋊ C7×Dic35
HallC3×C5 ⋊ C7×C13×Dic7
SylowC5 ⋊ C7×C13×Dic21
SylowC3 ⋊ C7×C13×Dic35

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D105
commutator, hypocenterC3×C5×C7C4×C7×C13
FrattiniC2C7×C13×D105
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C3×C5×C7C2×C7×C13
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C7×C13

144 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 68 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

9828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 369);