Finite Group Databasebeta

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C11×#16813405 #51432306

order39732
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#16813405

Splittings

derived, HallC7×C43 ⋊ C3×C4×C11
HallC11×Dic7×C43 ⋊ C3
HallC11×#11744749 ⋊ C4
HallC7×C11×C43 ⋊ C3×C4
HallDic7×C43 ⋊ C3×C11
Hall#11744749 ⋊ C4×C11
HallC11×C43 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×Dic7 ⋊ C43⋊C3
HallC7×C11 ⋊ C4×C43⋊C3
SylowC43 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallDic7 ⋊ C11×C43⋊C3
SylowC7 ⋊ C4×C11×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#14268592
commutator, hypocenterC7×C43C3×C4×C11
FrattiniC2C11×#14268592
Fitting, socleC2×C7×C11×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 44);