Finite Group Databasebeta

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C3×Dic199⋊C11 #39911052

order26268
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic199⋊C11
unambiguous semidirect product(C3×Dic199)⋊C11

Splittings

derived, SylowC199 ⋊ C3×C4×C11
HallC3×C199⋊C11 ⋊ C4
HallC3×Dic199 ⋊ C11
HallC199⋊C11 ⋊ C3×C4
HallDic199 ⋊ C3×C11
HallC3×C199 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3D199⋊C11
commutator, hypocenterC199C3×C4×C11
FrattiniC2C3×D199⋊C11
Fitting, socleC2×C3×C199C2×C11
prime radicalC2×C3×C199⋊C11C2
cosocleC2×C199C2×C3×C11
LCSG ▷ C199
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2388

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26268, 12);