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C3×C5×Dic407 #37567486

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic407

Splittings

derived, HallC11×C37 ⋊ C3×C4×C5
HallC3×C5×C11×C37 ⋊ C4
HallC5×C11×C37 ⋊ C3×C4
HallC3×C11×C37 ⋊ C4×C5
HallC3×C5×C37 ⋊ Dic11
HallC5×C37 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic37
HallC3×C37 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×Dic37
SylowC37 ⋊ C3×C5×Dic11
HallC3×C11 ⋊ C5×Dic37
SylowC11 ⋊ C3×C5×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D407
commutator, hypocenterC11×C37C3×C4×C5
FrattiniC2C3×C5×D407
Fitting, socle, prime radicalC2×C3×C5×C11×C37C2
cosocleC2×C11×C37C2×C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24420

Conjugacy classes & character table

6150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 7);