Finite Group Databasebeta

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C3×C11×Dic201 #40997644

order26532
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic201
unambiguous semidirect productC3⋊(C3×C11×Dic67)

Splittings

derivedC3×C67 ⋊ C3×C4×C11
HallC32×C11×C67 ⋊ C4
HallC11×C67 ⋊ C3×Dic3
HallC32×C67 ⋊ C4×C11
HallC32×C11 ⋊ Dic67
SylowC67 ⋊ C3×C11×Dic3
SylowC32 ⋊ C11×Dic67

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D201
commutator, hypocenterC3×C67C3×C4×C11
FrattiniC2C3×C11×D201
Fitting, socle, prime radicalC2×C32×C11×C67C2
cosocleC2×C3×C67C2×C3×C11
LCSG ▷ C3×C67
UCSC1 ◁ C2×C3×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8844

Conjugacy classes & character table

6732 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26532, 75);