Finite Group Databasebeta

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C2×C11×C157⋊C9 #44527255

order31086
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C157⋊C9
unambiguous semidirect product(C2×C157)⋊(C9×C11)
unambiguous semidirect product(C2×C11×C157)⋊C9

Splittings

derived, SylowC157 ⋊ C2×C9×C11
HallC2×C11×C157 ⋊ C9
HallC11×C157 ⋊ C2×C9
HallC2×C157 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C157⋊C3
commutator, hypocenterC157C2×C9×C11
FrattiniC3C2×C11×C157⋊C3
Fitting, socle, prime radicalC2×C3×C11×C157C3
cosocleC3×C157C2×C3×C11
LCSG ▷ C157
UCSC1 ◁ C2×C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31086

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31086, 2);