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C3×C5×Dic301 #31825334

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic301

Splittings

derived, HallC7×C43 ⋊ C3×C4×C5
HallC3×C5×C7×C43 ⋊ C4
HallC5×C7×C43 ⋊ C3×C4
HallC3×C7×C43 ⋊ C4×C5
HallC3×C5×C43 ⋊ Dic7
HallC5×C43 ⋊ C3×Dic7
HallC3×C43 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ Dic43
SylowC43 ⋊ C3×C5×Dic7
HallC5×C7 ⋊ C3×Dic43
HallC3×C7 ⋊ C5×Dic43
SylowC7 ⋊ C3×C5×Dic43

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D301
commutator, hypocenterC7×C43C3×C4×C5
FrattiniC2C3×C5×D301
Fitting, socle, prime radicalC2×C3×C5×C7×C43C2
cosocleC2×C7×C43C2×C3×C5
LCSG ▷ C7×C43
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18060

Conjugacy classes & character table

4560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 10);