Finite Group Databasebeta

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C5×C7×#66524⋊C2 #37552002

order23310
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×#66524⋊C2
unambiguous semidirect product#66524⋊(C2×C5×C7)

Splittings

derived, SylowC37 ⋊ C2×C5×C7×C9
HallC5×C7×#66524 ⋊ C2
HallC5×C7×D37 ⋊ C9
HallC7×#66524 ⋊ C2×C5
HallC5×#66524 ⋊ C2×C7
HallC5×C7×C37 ⋊ C2×C9
HallC7×D37 ⋊ C5×C9
HallC5×D37 ⋊ C7×C9
Hall#66524 ⋊ C2×C5×C7
HallC7×C37 ⋊ C2×C5×C9
HallC5×C37 ⋊ C2×C7×C9
HallD37 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7D37⋊C3
commutator, hypocenterC37C2×C5×C7×C9
FrattiniC3C5×C7×D37⋊C3
Fitting, socleC3×C5×C7×C37C2×C3
prime radicalC3×C5×C7×D37C3
cosocleC3×C37C2×C3×C5×C7
LCSG ▷ C37
UCSC1 ◁ C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11655

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 21);