Finite Group Databasebeta

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C5×C11×C19×Dic5 #35229871

order20900
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C19×Dic5

Splittings

derivedC5 ⋊ C4×C5×C11×C19
HallC52×C11×C19 ⋊ C4
HallC52×C19 ⋊ C4×C11
HallC52×C11 ⋊ C4×C19
SylowC52 ⋊ C4×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C19D5
commutator, hypocenterC5C4×C5×C11×C19
FrattiniC2C5×D5×C11×C19
Fitting, socle, prime radicalC2×C52×C11×C19C2
cosocleC2×C5C2×C5×C11×C19
LCSG ▷ C5
UCSC1 ◁ C2×C5×C11×C19

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

8360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20900, 53);