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C3×C5×Dic497 #44447121

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic497

Splittings

derived, HallC7×C71 ⋊ C3×C4×C5
HallC3×C5×C7×C71 ⋊ C4
HallC5×C7×C71 ⋊ C3×C4
HallC3×C7×C71 ⋊ C4×C5
HallC3×C5×C71 ⋊ Dic7
HallC5×C71 ⋊ C3×Dic7
HallC3×C71 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ Dic71
SylowC71 ⋊ C3×C5×Dic7
HallC5×C7 ⋊ C3×Dic71
HallC3×C7 ⋊ C5×Dic71
SylowC7 ⋊ C3×C5×Dic71

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D497
commutator, hypocenterC7×C71C3×C4×C5
FrattiniC2C3×C5×D497
Fitting, socle, prime radicalC2×C3×C5×C7×C71C2
cosocleC2×C7×C71C2×C3×C5
LCSG ▷ C7×C71
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29820

Conjugacy classes & character table

7500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 9);