Finite Group Databasebeta

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C3×Dic5×C97⋊C3 #31775520

order17460
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×Dic5×C97⋊C3
unambiguous semidirect product(Dic5×C97)⋊C32
unambiguous semidirect product(C3×Dic5×C97)⋊C3

Splittings

derived, HallC5×C97 ⋊ C32×C4
HallC3×C5×C97⋊C3 ⋊ C4
HallDic5×C97 ⋊ C32
SylowC97 ⋊ C32×Dic5
SylowC5 ⋊ C3×C4×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C97⋊C3
commutator, hypocenterC5×C97C32×C4
FrattiniC2C3×D5×C97⋊C3
Fitting, socleC2×C3×C5×C97C2×C3
prime radicalC2×C3×C5×C97⋊C3C2
cosocleC2×C5×C97C2×C32
LCSG ▷ C5×C97
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 56);