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C3×C23×D245 #46798904

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×D245
unambiguous semidirect productC5⋊(C3×C23×D49)

Splittings

Fitting, HallC3×C5×C23×C49 ⋊ C2
derived, HallC5×C49 ⋊ C2×C3×C23
HallC5×C23×C49 ⋊ C2×C3
HallC3×C23×C49 ⋊ D5
HallC23×C49 ⋊ C3×D5
HallC3×C5×C49 ⋊ C2×C23
HallC3×C5×C23 ⋊ D49
HallC3×C49 ⋊ D5×C23
HallC5×C23 ⋊ C3×D49
SylowC49 ⋊ C3×D5×C23
HallC3×C5 ⋊ C23×D49
SylowC5 ⋊ C3×C23×D49

Subgroups

subgroupG/H
center, hypercenterC3×C23D245
commutator, cosocle, hypocenterC5×C49C2×C3×C23
FrattiniC7C3×C23×D35
FittingC3×C5×C23×C49C2
socleC3×C5×C7×C23D7
LCSG ▷ C5×C49
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16905

Conjugacy classes & character table

8556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 8);