Finite Group Databasebeta

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Dic11×#11715913 #46803155

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

Aliases

direct productDic11×#11715913
unambiguous semidirect productC11⋊(C4×#11715913)

Splittings

derived, HallC7×C11×C37 ⋊ C3×C4
HallC7×C37×Dic11 ⋊ C3
HallC11×#11715913 ⋊ C4
HallC37×Dic11 ⋊ ΓL(1,𝔽8)
HallC11×C37 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic11 ⋊ C37⋊C3
HallC7×C37 ⋊ C3×Dic11
HallC7×C11 ⋊ C4×C37⋊C3
SylowC37 ⋊ ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ C4×#11715913
SylowC7 ⋊ Dic11×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D11×#11715913
commutator, hypocenterC7×C11×C37C3×C4
Fitting, socle, cosocleC2×C7×C11×C37C2×C3
prime radicalC2×C11×#11715913C2
LCSG ▷ C7×C11×C37
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

1246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 27);