Finite Group Databasebeta

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C5×D3×C11×C103 #46800923

order33990
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C103 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C103
unambiguous semidirect productC3⋊(C2×C5×C11×C103)

Splittings

Fitting, socle, HallC3×C5×C11×C103 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C11×C103
HallC3×C11×C103 ⋊ C2×C5
HallC3×C5×C103 ⋊ C2×C11
HallC3×C103 ⋊ C2×C5×C11
HallC3×C5×C11 ⋊ C2×C103
HallC3×C11 ⋊ C2×C5×C103
HallC3×C5 ⋊ C2×C11×C103

Subgroups

subgroupG/H
center, hypercenterC5×C11×C103D3
commutator, cosocle, hypocenterC3C2×C5×C11×C103
FrattiniC1G
Fitting, socleC3×C5×C11×C103C2
LCSG ▷ C3
UCSC1 ◁ C5×C11×C103

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16995

Conjugacy classes & character table

16995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33990, 12);