Finite Group Databasebeta

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C19×Dic11⋊C25 #35229829

order20900
automorphism?
homologyAbelianization (H1) = C4×C19×C25 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic11⋊C25
unambiguous semidirect productDic11⋊(C19×C25)
unambiguous semidirect product(C11⋊C25)⋊(C4×C19)
unambiguous semidirect product(C19×Dic11)⋊C25

Splittings

derived, SylowC11 ⋊ C4×C19×C25
HallC19×C11⋊C25 ⋊ C4
HallC19×Dic11 ⋊ C25
HallC11⋊C25 ⋊ C4×C19
HallC11×C19 ⋊ C4×C25
HallDic11 ⋊ C19×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19AGL(1,𝔽11)
commutator, hypocenterC11C4×C19×C25
FrattiniC2×C5C19×AGL(1,𝔽11)
Fitting, socle, prime radicalC2×C5×C11×C19C2×C5
cosocleC2×C5×C11C2×C5×C19
LCSG ▷ C11
UCSC1 ◁ C2×C5×C19

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20900

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 11);