Finite Group Databasebeta

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C3×Dic3311 #51432276

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

Aliases

direct productC3×Dic3311

Splittings

derived, HallC7×C11×C43 ⋊ C3×C4
HallC3×C7×C11×C43 ⋊ C4
HallC3×C11×C43 ⋊ Dic7
HallC3×C7×C43 ⋊ Dic11
HallC11×C43 ⋊ C3×Dic7
HallC7×C43 ⋊ C3×Dic11
HallC3×C7×C11 ⋊ Dic43
HallC3×C43 ⋊ Dic77
HallC7×C11 ⋊ C3×Dic43
SylowC43 ⋊ C3×Dic77
HallC3×C11 ⋊ Dic301
HallC3×C7 ⋊ Dic473
SylowC11 ⋊ C3×Dic301
SylowC7 ⋊ C3×Dic473

Subgroups

subgroupG/H
center, hypercenterC2×C3D3311
commutator, hypocenterC7×C11×C43C3×C4
FrattiniC2C3×D3311
Fitting, socleC2×C3×C7×C11×C43C2
LCSG ▷ C7×C11×C43
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9942 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(39732, 14);