Finite Group Databasebeta

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C32×C4×C67⋊C11 #40997629

order26532
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C4×C67⋊C11
unambiguous semidirect product(C32×C4×C67)⋊C11

Splittings

Fitting, HallC32×C4×C67 ⋊ C11
derived, SylowC67 ⋊ C32×C4×C11
HallC32×C67 ⋊ C4×C11
HallC4×C67 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC32×C4C67⋊C11
commutator, hypocenterC67C32×C4×C11
FrattiniC2C2×C32×C67⋊C11
FittingC32×C4×C67C11
socleC2×C32×C67C2×C11
prime radicalC2×C32×C67⋊C11C2
cosocleC2×C67C2×C32×C11
LCSG ▷ C67
UCSC1 ◁ C32×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2412

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26532, 60);