Finite Group Databasebeta

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Dic5×C13⋊#3862 #50303659

order38220
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productDic5×C13⋊#3862
unambiguous semidirect product(C13×Dic5)⋊#3862

Splittings

derived, HallC5×C72×C13 ⋊ C3×C4
HallC72×C13×Dic5 ⋊ C3
HallC5×C13⋊#3862 ⋊ C4
HallC72×Dic5 ⋊ C13⋊C3
HallC72×C13 ⋊ C3×Dic5
HallC13×Dic5 ⋊ #3862
HallC5×C72 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C4×#3862
SylowC72 ⋊ Dic5×C13⋊C3
SylowC13 ⋊ Dic5×#3862
SylowC5 ⋊ C4×C13⋊#3862

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×C13⋊#3862
commutator, hypocenterC5×C72×C13C3×C4
Fitting, socle, cosocleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C13⋊#3862C2
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

120 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 45 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

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 345);