Finite Group Databasebeta

← Prev (#38784273) Next (#38784275) →

C2×C5×C23×C37⋊C3 #38784274

order25530
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C23×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C3×C5×C23)
unambiguous semidirect product(C2×C5×C37)⋊(C3×C23)
unambiguous semidirect product(C2×C23×C37)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C23×C37)⋊C3

Splittings

Fitting, socle, HallC2×C5×C23×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C5×C23
HallC5×C23×C37 ⋊ C2×C3
HallC2×C23×C37 ⋊ C3×C5
HallC23×C37 ⋊ C2×C3×C5
HallC2×C5×C37 ⋊ C3×C23
HallC5×C37 ⋊ C2×C3×C23
HallC2×C37 ⋊ C3×C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23C37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C23
FrattiniC1G
Fitting, socleC2×C5×C23×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8510

Conjugacy classes & character table

3450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25530, 2);