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C3×C11⋊C5×D97 #44544970

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×D97
unambiguous semidirect product(C3×C11×D97)⋊C5

Splittings

Fitting, socle, HallC3×C11×C97 ⋊ C2×C5
derived, HallC11×C97 ⋊ C2×C3×C5
HallC3×C11⋊C5×C97 ⋊ C2
HallC3×C11×D97 ⋊ C5
HallC11⋊C5×C97 ⋊ C2×C3
HallC11×D97 ⋊ C3×C5
HallC3×C97 ⋊ C2×C11⋊C5
SylowC97 ⋊ C2×C3×C11⋊C5
HallC3×C11 ⋊ C5×D97
SylowC11 ⋊ C3×C5×D97

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D97
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C97C2×C5
LCSG ▷ C11×C97
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3201

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 20);