Finite Group Databasebeta

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C3×C5×C11×D97 #44544955

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D97

Splittings

Fitting, socle, HallC3×C5×C11×C97 ⋊ C2
derived, SylowC97 ⋊ C2×C3×C5×C11
HallC5×C11×C97 ⋊ C2×C3
HallC3×C11×C97 ⋊ C2×C5
HallC3×C5×C97 ⋊ C2×C11
HallC11×C97 ⋊ C2×C3×C5
HallC5×C97 ⋊ C2×C3×C11
HallC3×C97 ⋊ C2×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D97
commutator, cosocle, hypocenterC97C2×C3×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C97C2
LCSG ▷ C97
UCSC1 ◁ C3×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16005

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 5);