Finite Group Databasebeta

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C2×C5×C11×C97⋊C3 #44544953

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

Aliases

direct productC2×C5×C11×C97⋊C3
unambiguous semidirect product(C2×C97)⋊(C3×C5×C11)
unambiguous semidirect product(C2×C5×C97)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C97)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C97 ⋊ C3
derived, SylowC97 ⋊ C2×C3×C5×C11
HallC5×C11×C97 ⋊ C2×C3
HallC2×C11×C97 ⋊ C3×C5
HallC11×C97 ⋊ C2×C3×C5
HallC2×C5×C97 ⋊ C3×C11
HallC5×C97 ⋊ C2×C3×C11
HallC2×C97 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C97⋊C3
commutator, cosocle, hypocenterC97C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C97C3
LCSG ▷ C97
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10670

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 3);