Finite Group Databasebeta

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C72×Dic65⋊C3 #50303607

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C72)

Splittings

derived, HallC5×C13 ⋊ C3×C4×C72
HallC72×Dic65 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC72×C13⋊C3 ⋊ Dic5
HallC72×C13 ⋊ C3×Dic5
HallDic65 ⋊ C3×C72
HallC5×C72 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C4×C72
HallC13⋊C3 ⋊ C72×Dic5
SylowC13 ⋊ C3×C72×Dic5
SylowC5 ⋊ C72×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C72C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C72
FrattiniC2C72×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C72×C13⋊C3C2
cosocleC2×C5×C13C2×C3×C72
LCSG ▷ C5×C13
UCSC1 ◁ C2×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12740

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 293);