Finite Group Databasebeta

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C4×C9×C67⋊C11 #40997571

order26532
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C67⋊C11
unambiguous semidirect product(C4×C9×C67)⋊C11

Splittings

Fitting, HallC4×C9×C67 ⋊ C11
derived, SylowC67 ⋊ C4×C9×C11
HallC9×C67 ⋊ C4×C11
HallC4×C67 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC4×C9C67⋊C11
commutator, hypocenterC67C4×C9×C11
FrattiniC2×C3C2×C3×C67⋊C11
FittingC4×C9×C67C11
socle, cosocleC2×C3×C67C2×C3×C11
prime radicalC2×C3×C67⋊C11C2×C3
LCSG ▷ C67
UCSC1 ◁ C4×C9

36 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, 2);