Finite Group Databasebeta

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C11×Dic3×C169 #36373222

order22308
automorphism?
homologyAbelianization (H1) = C4×C11×C169 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic3×C169
unambiguous semidirect productC3⋊(C4×C11×C169)

Splittings

derived, SylowC3 ⋊ C4×C11×C169
HallC3×C11×C169 ⋊ C4
HallC3×C169 ⋊ C4×C11
HallC3×C11 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC2×C11×C169D3
commutator, hypocenterC3C4×C11×C169
FrattiniC2×C13D3×C11×C13
FittingC2×C3×C11×C169C2
socle, prime radicalC2×C3×C11×C13C2×C13
cosocleC2×C3×C13C2×C11×C13
LCSG ▷ C3
UCSC1 ◁ C2×C11×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22308

Conjugacy classes & character table

11154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22308, 9);