Finite Group Databasebeta

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C5×(C11⋊C5)⋊Dic31 #46802006

order34100
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(C11⋊C5)⋊Dic31
unambiguous semidirect product(C11⋊C5)⋊(C5×Dic31)

Splittings

derived, HallC11×C31 ⋊ C4×C52
HallC5×C31×C11⋊C5 ⋊ C4
HallDic341 ⋊ C52
HallC5×C11⋊C5 ⋊ Dic31
SylowC31 ⋊ C5×Dic11⋊C5
SylowC11 ⋊ C52×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C5(C11⋊C5)⋊D31
commutator, hypocenterC11×C31C4×C52
FrattiniC2C5×(C11⋊C5)⋊D31
Fitting, socleC2×C5×C11×C31C2×C5
prime radicalC2×C5×C31×C11⋊C5C2
cosocleC2×C11×C31C2×C52
LCSG ▷ C11×C31
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34100, 97);