Finite Group Databasebeta

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C4×(C199⋊C3)⋊C11 #39911044

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

Aliases

direct productC4×(C199⋊C3)⋊C11
unambiguous semidirect product(C4×C199⋊C3)⋊C11
unambiguous semidirect product(C4×C199⋊C11)⋊C3

Splittings

Fitting, HallC4×C199 ⋊ C3×C11
derived, SylowC199 ⋊ C3×C4×C11
HallC4×C199⋊C11 ⋊ C3
HallC4×C199⋊C3 ⋊ C11
HallC199⋊C11 ⋊ C3×C4
HallC199⋊C3 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC4(C199⋊C3)⋊C11
commutator, hypocenterC199C3×C4×C11
FrattiniC2C2×(C199⋊C3)⋊C11
FittingC4×C199C3×C11
socle, cosocleC2×C199C2×C3×C11
prime radicalC2×(C199⋊C3)⋊C11C2
LCSG ▷ C199
UCSC1 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 796

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26268, 4);