Finite Group Databasebeta

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C4×C17×C181⋊C3 #49147334

order36924
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C181⋊C3
unambiguous semidirect product(C4×C181)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C181)⋊C3

Splittings

Fitting, HallC4×C17×C181 ⋊ C3
derived, SylowC181 ⋊ C3×C4×C17
HallC17×C181 ⋊ C3×C4
HallC4×C181 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C181⋊C3
commutator, hypocenterC181C3×C4×C17
FrattiniC2C2×C17×C181⋊C3
FittingC4×C17×C181C3
socleC2×C17×C181C2×C3
prime radicalC2×C17×C181⋊C3C2
cosocleC2×C181C2×C3×C17
LCSG ▷ C181
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12308

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36924, 2);