Finite Group Databasebeta

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C32×D5×C373 #46777073

order33570
automorphism?
homologyAbelianization (H1) = C2×C32×C373 · Schur multiplier (H2) = C3

Aliases

direct productC32×D5×C373
unambiguous semidirect productC5⋊(C2×C32×C373)

Splittings

Fitting, socle, HallC32×C5×C373 ⋊ C2
derived, SylowC5 ⋊ C2×C32×C373
HallC5×C373 ⋊ C2×C32
HallC32×C5 ⋊ C2×C373

Subgroups

subgroupG/H
center, hypercenterC32×C373D5
commutator, cosocle, hypocenterC5C2×C32×C373
FrattiniC1G
Fitting, socleC32×C5×C373C2
LCSG ▷ C5
UCSC1 ◁ C32×C373

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16785

Conjugacy classes & character table

13428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33570, 23);