Finite Group Databasebeta

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C49⋊C3×Dic55 #44568329

order32340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC49⋊C3×Dic55
unambiguous semidirect productC11⋊(Dic5×C49⋊C3)
unambiguous semidirect product(C49×Dic55)⋊C3

Splittings

derived, HallC5×C11×C49 ⋊ C3×C4
HallC49×Dic55 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC11×C49⋊C3 ⋊ Dic5
HallC5×C49⋊C3 ⋊ Dic11
HallC11×C49 ⋊ C3×Dic5
HallC5×C49 ⋊ C3×Dic11
HallC5×C11 ⋊ C4×C49⋊C3
SylowC49 ⋊ C3×Dic55
SylowC11 ⋊ Dic5×C49⋊C3
SylowC5 ⋊ Dic11×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2D55×C49⋊C3
commutator, hypocenterC5×C11×C49C3×C4
FrattiniC2×C7ΓL(1,𝔽8)×D55
Fitting, cosocleC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11C2×ΓL(1,𝔽8)
prime radicalC2×C5×C11×C49⋊C3C2
LCSG ▷ C5×C11×C49
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 31);