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C11×(C43⋊C3)⋊Dic7 #51432308

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

Aliases

direct productC11×(C43⋊C3)⋊Dic7

Splittings

derived, HallC7×C43 ⋊ C3×C4×C11
HallC11×Dic301 ⋊ C3
HallC7×C11×C43⋊C3 ⋊ C4
HallC7×C11×C43 ⋊ C3×C4
HallC11×C43⋊C3 ⋊ Dic7
HallDic301 ⋊ C3×C11
HallC7×C43⋊C3 ⋊ C4×C11
HallC11×C43 ⋊ C3×Dic7
HallC43⋊C3 ⋊ C11×Dic7
HallC7×C11 ⋊ (C43⋊C3)⋊C4
SylowC43 ⋊ C3×C11×Dic7
SylowC7 ⋊ C11×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C11(C43⋊C3)⋊D7
commutator, hypocenterC7×C43C3×C4×C11
FrattiniC2C11×(C43⋊C3)⋊D7
Fitting, socleC2×C7×C11×C43C2×C3
LCSG ▷ C7×C43
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 46);