Finite Group Databasebeta

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C5×C11⋊C5×Dic29 #44542015

order31900
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×Dic29
unambiguous semidirect product(C11×Dic29)⋊C52
unambiguous semidirect product(C5×C11×Dic29)⋊C5

Splittings

derived, HallC11×C29 ⋊ C4×C52
HallC5×C29×C11⋊C5 ⋊ C4
HallC11×Dic29 ⋊ C52
SylowC29 ⋊ C4×C5×C11⋊C5
SylowC11 ⋊ C52×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊C5×D29
commutator, hypocenterC11×C29C4×C52
FrattiniC2C5×C11⋊C5×D29
Fitting, socleC2×C5×C11×C29C2×C5
prime radicalC2×C5×C29×C11⋊C5C2
cosocleC2×C11×C29C2×C52
LCSG ▷ C11×C29
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 50);