Finite Group Databasebeta

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C3⋊(C7⋊Dic385) #44568516

order32340
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C7

Aliases

unambiguous semidirect productC3⋊(C7⋊Dic385)
unambiguous semidirect productC7⋊Dic1155
unambiguous semidirect productC11⋊(C3⋊(C7⋊Dic35))

Splittings

derived, HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ Dic5
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ Dic15
HallC5×C72 ⋊ Dic33
HallC3×C5×C11 ⋊ C7⋊Dic7
HallC3×C72 ⋊ Dic55
HallC5×C11 ⋊ C3⋊(C7⋊Dic7)
SylowC72 ⋊ Dic165
HallC3×C11 ⋊ C7⋊Dic35
HallC3×C5 ⋊ C7⋊Dic77
SylowC11 ⋊ C3⋊(C7⋊Dic35)
SylowC5 ⋊ C3⋊(C7⋊Dic77)
SylowC3 ⋊ C7⋊Dic385

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C5⋊(C7⋊D77))
commutator, hypocenterC3×C5×C72×C11C4
Fitting, socle, prime radical, cosocleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C5×C72×C11
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Polycyclic presentation:

2,3,5,7^2,11,2|a^2=g,b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^10

Conjugacy classes & character table

8088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 218);