Finite Group Databasebeta

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C2×C43⋊C3×C23⋊C11 #72179409

order65274
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C43⋊C3×C23⋊C11

Splittings

Fitting, socle, HallC2×C23×C43 ⋊ C3×C11
derived, HallC23×C43 ⋊ C2×C3×C11
HallC2×C43×C23⋊C11 ⋊ C3
HallC43×C23⋊C11 ⋊ C2×C3
HallC2×C23×C43⋊C3 ⋊ C11
HallC23×C43⋊C3 ⋊ C2×C11
HallC2×C43 ⋊ C3×C23⋊C11
HallC2×C23 ⋊ C11×C43⋊C3
SylowC43 ⋊ C2×C3×C23⋊C11
SylowC23 ⋊ C2×C11×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C43⋊C3×C23⋊C11
commutator, cosocle, hypocenterC23×C43C2×C3×C11
FrattiniC1G
Fitting, socleC2×C23×C43C3×C11
LCSG ▷ C23×C43
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(65274, 4);