Finite Group Databasebeta

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C2×C5×#14556423 #37552061

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

Aliases

direct productC2×C5×#14556423

Splittings

Fitting, socle, HallC2×C5×C7×C37 ⋊ C9
derived, HallC7×C37 ⋊ C2×C5×C9
HallC5×C7×C37 ⋊ C2×C9
HallC2×C7×C37 ⋊ C5×C9
HallC2×C5×C37 ⋊ C7⋊C9
HallC5×C37 ⋊ C2×C7⋊C9
HallC2×C37 ⋊ C5×C7⋊C9
HallC2×C5×C7 ⋊ #66526
SylowC37 ⋊ C2×C5×C7⋊C9
HallC5×C7 ⋊ C2×#66526
HallC2×C7 ⋊ C5×#66526
SylowC7 ⋊ C2×C5×#66526

Subgroups

subgroupG/H
center, hypercenterC2×C5#14556423
commutator, hypocenterC7×C37C2×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C7×C37C9
prime radicalC2×C5×C7×C37⋊C3C3
cosocleC7×C37⋊C3C2×C3×C5
LCSG ▷ C7×C37
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2590

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 80);