Finite Group Databasebeta

← Prev (#46803132) Next (#46803134) →

C4×C11×#11715912 #46803133

order34188
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×#11715912

Splittings

Fitting, HallC4×C7×C11×C37 ⋊ C3
derived, HallC7×C37 ⋊ C3×C4×C11
HallC7×C11×C37 ⋊ C3×C4
HallC4×C11×C37 ⋊ ΓL(1,𝔽8)
HallC4×C7×C37 ⋊ C3×C11
HallC11×C37 ⋊ C4×ΓL(1,𝔽8)
HallC4×C7×C11 ⋊ C37⋊C3
HallC4×C37 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C4×C37⋊C3
SylowC37 ⋊ C4×C11×ΓL(1,𝔽8)
HallC4×C7 ⋊ C11×C37⋊C3
SylowC7 ⋊ C4×C11×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C11#11715912
commutator, hypocenterC7×C37C3×C4×C11
FrattiniC2C2×C11×#11715912
FittingC4×C7×C11×C37C3
socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×#11715912C2
cosocleC2×C7×C37C2×C3×C11
LCSG ▷ C7×C37
UCSC1 ◁ C4×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

3916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 5);