Finite Group Databasebeta

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C5×C23×C109⋊C3 #49178223

order37605
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×C109⋊C3
unambiguous semidirect productC109⋊(C3×C5×C23)
unambiguous semidirect product(C5×C109)⋊(C3×C23)
unambiguous semidirect product(C23×C109)⋊(C3×C5)
unambiguous semidirect product(C5×C23×C109)⋊C3

Splittings

Fitting, socle, HallC5×C23×C109 ⋊ C3
derived, SylowC109 ⋊ C3×C5×C23
HallC23×C109 ⋊ C3×C5
HallC5×C109 ⋊ C3×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23C109⋊C3
commutator, cosocle, hypocenterC109C3×C5×C23
FrattiniC1G
Fitting, socleC5×C23×C109C3
LCSG ▷ C109
UCSC1 ◁ C5×C23

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12535

Conjugacy classes & character table

4485 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37605, 2);