Finite Group Databasebeta

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C5×C11×Dic3×C37 #37567491

order24420
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic3×C37
unambiguous semidirect productC3⋊(C4×C5×C11×C37)

Splittings

derived, SylowC3 ⋊ C4×C5×C11×C37
HallC3×C5×C11×C37 ⋊ C4
HallC3×C11×C37 ⋊ C4×C5
HallC3×C5×C37 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C37
HallC3×C37 ⋊ C4×C5×C11
HallC3×C11 ⋊ C4×C5×C37
HallC3×C5 ⋊ C4×C11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C37D3
commutator, hypocenterC3C4×C5×C11×C37
FrattiniC2C5×D3×C11×C37
Fitting, socle, prime radicalC2×C3×C5×C11×C37C2
cosocleC2×C3C2×C5×C11×C37
LCSG ▷ C3
UCSC1 ◁ C2×C5×C11×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24420

Conjugacy classes & character table

12210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 12);