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C3×C7×Dic295 #37613345

order24780
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic295
unambiguous semidirect productC59⋊(C3×C7×Dic5)

Splittings

derived, HallC5×C59 ⋊ C3×C4×C7
HallC3×C5×C7×C59 ⋊ C4
HallC5×C7×C59 ⋊ C3×C4
HallC3×C7×C59 ⋊ Dic5
HallC3×C5×C59 ⋊ C4×C7
HallC7×C59 ⋊ C3×Dic5
HallC3×C59 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ Dic59
SylowC59 ⋊ C3×C7×Dic5
HallC5×C7 ⋊ C3×Dic59
HallC3×C5 ⋊ C7×Dic59
SylowC5 ⋊ C3×C7×Dic59

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D295
commutator, hypocenterC5×C59C3×C4×C7
FrattiniC2C3×C7×D295
Fitting, socle, prime radicalC2×C3×C5×C7×C59C2
cosocleC2×C5×C59C2×C3×C7
LCSG ▷ C5×C59
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24780

Conjugacy classes & character table

6258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 7);